diff --git a/Mathematics/1st/Fundamentals_of_mathematics/Images/complement.pdf b/Mathematics/1st/Fundamentals_of_mathematics/Images/complement.pdf index c19a50e..17f70a0 100644 Binary files a/Mathematics/1st/Fundamentals_of_mathematics/Images/complement.pdf and b/Mathematics/1st/Fundamentals_of_mathematics/Images/complement.pdf differ diff --git a/Mathematics/1st/Fundamentals_of_mathematics/Images/complement.tex b/Mathematics/1st/Fundamentals_of_mathematics/Images/complement.tex index 187f70a..5e95945 100644 --- a/Mathematics/1st/Fundamentals_of_mathematics/Images/complement.tex +++ b/Mathematics/1st/Fundamentals_of_mathematics/Images/complement.tex @@ -1,5 +1,5 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} \begin{document} diff --git a/Mathematics/1st/Fundamentals_of_mathematics/Images/difference.pdf b/Mathematics/1st/Fundamentals_of_mathematics/Images/difference.pdf index 719dd42..987aaf2 100644 Binary files a/Mathematics/1st/Fundamentals_of_mathematics/Images/difference.pdf and b/Mathematics/1st/Fundamentals_of_mathematics/Images/difference.pdf differ diff --git a/Mathematics/1st/Fundamentals_of_mathematics/Images/difference.tex b/Mathematics/1st/Fundamentals_of_mathematics/Images/difference.tex index cfe752b..12ff7e3 100644 --- a/Mathematics/1st/Fundamentals_of_mathematics/Images/difference.tex +++ b/Mathematics/1st/Fundamentals_of_mathematics/Images/difference.tex @@ -1,5 +1,5 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} \begin{document} @@ -18,6 +18,5 @@ % Set intersection label \node at (-0.6,0) {$A\setminus B$}; - \end{tikzpicture} \end{document} \ No newline at end of file diff --git a/Mathematics/1st/Fundamentals_of_mathematics/Images/intersection.pdf b/Mathematics/1st/Fundamentals_of_mathematics/Images/intersection.pdf index 3f8b0ba..77c198e 100644 Binary files a/Mathematics/1st/Fundamentals_of_mathematics/Images/intersection.pdf and b/Mathematics/1st/Fundamentals_of_mathematics/Images/intersection.pdf differ diff --git a/Mathematics/1st/Fundamentals_of_mathematics/Images/intersection.tex b/Mathematics/1st/Fundamentals_of_mathematics/Images/intersection.tex index 490b63a..bcdb73a 100644 --- a/Mathematics/1st/Fundamentals_of_mathematics/Images/intersection.tex +++ b/Mathematics/1st/Fundamentals_of_mathematics/Images/intersection.tex @@ -1,5 +1,5 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} \begin{document} diff --git a/Mathematics/1st/Fundamentals_of_mathematics/Images/union.pdf b/Mathematics/1st/Fundamentals_of_mathematics/Images/union.pdf index bfa58ea..fad675f 100644 Binary files a/Mathematics/1st/Fundamentals_of_mathematics/Images/union.pdf and b/Mathematics/1st/Fundamentals_of_mathematics/Images/union.pdf differ diff --git a/Mathematics/1st/Fundamentals_of_mathematics/Images/union.tex b/Mathematics/1st/Fundamentals_of_mathematics/Images/union.tex index c205ea3..58d7f70 100644 --- a/Mathematics/1st/Fundamentals_of_mathematics/Images/union.tex +++ b/Mathematics/1st/Fundamentals_of_mathematics/Images/union.tex @@ -1,5 +1,5 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} \begin{document} diff --git a/Mathematics/1st/Linear_algebra/Images/first_isomorphism.pdf b/Mathematics/1st/Linear_algebra/Images/first_isomorphism.pdf index 781578a..f11cace 100644 Binary files a/Mathematics/1st/Linear_algebra/Images/first_isomorphism.pdf and b/Mathematics/1st/Linear_algebra/Images/first_isomorphism.pdf differ diff --git a/Mathematics/1st/Linear_algebra/Images/first_isomorphism.tex b/Mathematics/1st/Linear_algebra/Images/first_isomorphism.tex index 80fa521..e6aea75 100644 --- a/Mathematics/1st/Linear_algebra/Images/first_isomorphism.tex +++ b/Mathematics/1st/Linear_algebra/Images/first_isomorphism.tex @@ -1,16 +1,17 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} +\usepackage{../../../../preamble_math} \begin{document} \begin{tikzpicture} - %%% NODES - \path (0,0) node(x) {$U$} - (2,0) node(y) {$\im f$} (0,-2) node(z) {$\displaystyle\quot{U}{\ker f}$}; - %%% LINES - \draw[very thin,->] (x) --node[above,midway] {$f$} (y); - \draw[very thin,->] (z) --node[right,pos=0.45] {$\tilde{f}$} (y); - \draw[very thin,->] (x) --node[left,midway] {$\pi$} (z); + %%% NODES + \path (0,0) node(x) {$U$} + (2,0) node(y) {$\im f$} (0,-2) node(z) {$\displaystyle\quot{U}{\ker f}$}; + %%% LINES + \draw[very thin,->] (x) --node[above,midway] {$f$} (y); + \draw[very thin,->] (z) --node[right,pos=0.45] {$\tilde{f}$} (y); + \draw[very thin,->] (x) --node[left,midway] {$\pi$} (z); \end{tikzpicture} \end{document} \ No newline at end of file diff --git a/Mathematics/1st/Real-valued_functions/Images/concavity.pdf b/Mathematics/1st/Real-valued_functions/Images/concavity.pdf index da263ad..5685047 100644 Binary files a/Mathematics/1st/Real-valued_functions/Images/concavity.pdf and b/Mathematics/1st/Real-valued_functions/Images/concavity.pdf differ diff --git a/Mathematics/1st/Real-valued_functions/Images/concavity.tex b/Mathematics/1st/Real-valued_functions/Images/concavity.tex index bbcc470..9d5f93a 100644 --- a/Mathematics/1st/Real-valued_functions/Images/concavity.tex +++ b/Mathematics/1st/Real-valued_functions/Images/concavity.tex @@ -1,11 +1,11 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} \begin{document} \begin{tikzpicture} - \begin{axis}[xmin=-1,xmax=1,ymin=0,ymax=2, - axis equal image] - \addplot [thin,samples=200,smooth,blue] {2-2*x*x}; - \end{axis} + \begin{axis}[xmin=-1,xmax=1,ymin=0,ymax=2, + axis equal image] + \addplot [thin,samples=200,smooth,blue] {2-2*x*x}; + \end{axis} \end{tikzpicture} \end{document} \ No newline at end of file diff --git a/Mathematics/1st/Real-valued_functions/Images/convexity.pdf b/Mathematics/1st/Real-valued_functions/Images/convexity.pdf index 7ecb8fa..e22d5df 100644 Binary files a/Mathematics/1st/Real-valued_functions/Images/convexity.pdf and b/Mathematics/1st/Real-valued_functions/Images/convexity.pdf differ diff --git a/Mathematics/1st/Real-valued_functions/Images/convexity.tex b/Mathematics/1st/Real-valued_functions/Images/convexity.tex index 678e5f1..a9acc38 100644 --- a/Mathematics/1st/Real-valued_functions/Images/convexity.tex +++ b/Mathematics/1st/Real-valued_functions/Images/convexity.tex @@ -1,11 +1,11 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} \begin{document} \begin{tikzpicture} - \begin{axis}[xmin=-1,xmax=1,ymin=0,ymax=2, - axis equal image] - \addplot [thin,samples=200,smooth,blue] {2*x*x}; - \end{axis} + \begin{axis}[xmin=-1,xmax=1,ymin=0,ymax=2, + axis equal image] + \addplot [thin,samples=200,smooth,blue] {2*x*x}; + \end{axis} \end{tikzpicture} \end{document} \ No newline at end of file diff --git a/Mathematics/1st/Real-valued_functions/Images/discontinuity1.pdf b/Mathematics/1st/Real-valued_functions/Images/discontinuity1.pdf index 0202d9e..c068c44 100644 Binary files a/Mathematics/1st/Real-valued_functions/Images/discontinuity1.pdf and b/Mathematics/1st/Real-valued_functions/Images/discontinuity1.pdf differ diff --git a/Mathematics/1st/Real-valued_functions/Images/discontinuity1.tex b/Mathematics/1st/Real-valued_functions/Images/discontinuity1.tex index 44fb1a5..0b901ac 100644 --- a/Mathematics/1st/Real-valued_functions/Images/discontinuity1.tex +++ b/Mathematics/1st/Real-valued_functions/Images/discontinuity1.tex @@ -1,13 +1,13 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} \begin{document} \begin{tikzpicture} - \begin{axis}[xmin=0,xmax=1,ymin=0,ymax=1, - axis equal image] - \addplot [thin,samples=200,smooth,blue] {x*x}; - \draw [blue,fill=white] (axis cs:0.5,0.25) circle [radius=1.5pt]; - \draw [blue,fill=blue] (axis cs:0.5,0.5) circle [radius=1.5pt]; - \end{axis} + \begin{axis}[xmin=0,xmax=1,ymin=0,ymax=1, + axis equal image] + \addplot [thin,samples=200,smooth,blue] {x*x}; + \draw [blue,fill=white] (axis cs:0.5,0.25) circle [radius=1.5pt]; + \draw [blue,fill=blue] (axis cs:0.5,0.5) circle [radius=1.5pt]; + \end{axis} \end{tikzpicture} \end{document} \ No newline at end of file diff --git a/Mathematics/1st/Real-valued_functions/Images/discontinuity2.pdf b/Mathematics/1st/Real-valued_functions/Images/discontinuity2.pdf index 523c46c..60ac13a 100644 Binary files a/Mathematics/1st/Real-valued_functions/Images/discontinuity2.pdf and b/Mathematics/1st/Real-valued_functions/Images/discontinuity2.pdf differ diff --git a/Mathematics/1st/Real-valued_functions/Images/discontinuity2.tex b/Mathematics/1st/Real-valued_functions/Images/discontinuity2.tex index 9fbd527..44a2141 100644 --- a/Mathematics/1st/Real-valued_functions/Images/discontinuity2.tex +++ b/Mathematics/1st/Real-valued_functions/Images/discontinuity2.tex @@ -1,14 +1,14 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} \begin{document} \begin{tikzpicture} - \begin{axis}[xmin=0,xmax=1,ymin=0,ymax=1, - axis equal image] - \addplot [thin,samples=200,smooth,blue,domain=0:0.5] {x*x}; - \addplot [thin,samples=200,smooth,blue,domain=0.5:1] {0.75-(x-1)^2}; - \draw [blue,fill=white] (axis cs:0.5,0.25) circle [radius=1.5pt]; - \draw [blue,fill=blue] (axis cs:0.5,0.5) circle [radius=1.5pt]; - \end{axis} + \begin{axis}[xmin=0,xmax=1,ymin=0,ymax=1, + axis equal image] + \addplot [thin,samples=200,smooth,blue,domain=0:0.5] {x*x}; + \addplot [thin,samples=200,smooth,blue,domain=0.5:1] {0.75-(x-1)^2}; + \draw [blue,fill=white] (axis cs:0.5,0.25) circle [radius=1.5pt]; + \draw [blue,fill=blue] (axis cs:0.5,0.5) circle [radius=1.5pt]; + \end{axis} \end{tikzpicture} \end{document} \ No newline at end of file diff --git a/Mathematics/1st/Real-valued_functions/Images/discontinuity3.pdf b/Mathematics/1st/Real-valued_functions/Images/discontinuity3.pdf index 4525d65..534bf83 100644 Binary files a/Mathematics/1st/Real-valued_functions/Images/discontinuity3.pdf and b/Mathematics/1st/Real-valued_functions/Images/discontinuity3.pdf differ diff --git a/Mathematics/1st/Real-valued_functions/Images/discontinuity3.tex b/Mathematics/1st/Real-valued_functions/Images/discontinuity3.tex index f0cc4ff..faabe7e 100644 --- a/Mathematics/1st/Real-valued_functions/Images/discontinuity3.tex +++ b/Mathematics/1st/Real-valued_functions/Images/discontinuity3.tex @@ -1,13 +1,13 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} \begin{document} \begin{tikzpicture} - \begin{axis}[xmin=0,xmax=1,ymin=0,ymax=1, - axis equal image] - \addplot [thin,samples=200,smooth,blue,domain=0:0.49] {-1/(155*(0.5-x))+0.5}; - \addplot [thin,samples=200,smooth,blue,domain=0.51:1] {1/(155*(x-0.5))+0.5}; - \draw [thin,blue,dashed] (axis cs:0.5,0) -- (axis cs:0.5,1); - \end{axis} + \begin{axis}[xmin=0,xmax=1,ymin=0,ymax=1, + axis equal image] + \addplot [thin,samples=200,smooth,blue,domain=0:0.49] {-1/(155*(0.5-x))+0.5}; + \addplot [thin,samples=200,smooth,blue,domain=0.51:1] {1/(155*(x-0.5))+0.5}; + \draw [thin,blue,dashed] (axis cs:0.5,0) -- (axis cs:0.5,1); + \end{axis} \end{tikzpicture} \end{document} \ No newline at end of file diff --git a/Mathematics/1st/Real-valued_functions/Images/discontinuity4.pdf b/Mathematics/1st/Real-valued_functions/Images/discontinuity4.pdf index 0106392..863b62d 100644 Binary files a/Mathematics/1st/Real-valued_functions/Images/discontinuity4.pdf and b/Mathematics/1st/Real-valued_functions/Images/discontinuity4.pdf differ diff --git a/Mathematics/1st/Real-valued_functions/Images/discontinuity4.tex b/Mathematics/1st/Real-valued_functions/Images/discontinuity4.tex index abb15a4..561f826 100644 --- a/Mathematics/1st/Real-valued_functions/Images/discontinuity4.tex +++ b/Mathematics/1st/Real-valued_functions/Images/discontinuity4.tex @@ -1,17 +1,17 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} \begin{document} \begin{tikzpicture} - \begin{axis}[xmin=0,xmax=1,ymin=0,ymax=1, - axis equal image] - \addplot [thin,samples=200,smooth,blue,domain=0.2:1] {0.25 * sin(deg(1/x))+0.5}; - \addplot [thin,samples=2000,smooth,blue,domain=0.1:0.2] {0.25 * sin(deg(1/x))+0.5}; - \addplot [thin,samples=1000,smooth,blue,domain=0.07:0.1] {0.25 * sin(deg(1/x))+0.5}; - \addplot [thin,samples=1000,smooth,blue,domain=0.05:0.7] {0.25 * sin(deg(1/x))+0.5}; - \addplot [thin,samples=1000,smooth,blue,domain=0.03:0.5] {0.25 * sin(deg(1/x))+0.5}; - \addplot [thin,samples=2000,smooth,blue,domain=0.019:0.3] {0.25 * sin(deg(1/x))+0.5}; - \draw [rounded corners=0.1pt,thin,blue,fill=blue] (0.0025,0.75) rectangle (0.019,0.25); - \end{axis} + \begin{axis}[xmin=0,xmax=1,ymin=0,ymax=1, + axis equal image] + \addplot [thin,samples=200,smooth,blue,domain=0.2:1] {0.25 * sin(deg(1/x))+0.5}; + \addplot [thin,samples=2000,smooth,blue,domain=0.1:0.2] {0.25 * sin(deg(1/x))+0.5}; + \addplot [thin,samples=1000,smooth,blue,domain=0.07:0.1] {0.25 * sin(deg(1/x))+0.5}; + \addplot [thin,samples=1000,smooth,blue,domain=0.05:0.7] {0.25 * sin(deg(1/x))+0.5}; + \addplot [thin,samples=1000,smooth,blue,domain=0.03:0.5] {0.25 * sin(deg(1/x))+0.5}; + \addplot [thin,samples=2000,smooth,blue,domain=0.019:0.3] {0.25 * sin(deg(1/x))+0.5}; + \draw [rounded corners=0.1pt,thin,blue,fill=blue] (0.0025,0.75) rectangle (0.019,0.25); + \end{axis} \end{tikzpicture} \end{document} \ No newline at end of file diff --git a/Mathematics/1st/Real-valued_functions/Images/lower_sum.pdf b/Mathematics/1st/Real-valued_functions/Images/lower_sum.pdf index f27e921..479a35f 100644 Binary files a/Mathematics/1st/Real-valued_functions/Images/lower_sum.pdf and b/Mathematics/1st/Real-valued_functions/Images/lower_sum.pdf differ diff --git a/Mathematics/1st/Real-valued_functions/Images/lower_sum.tex b/Mathematics/1st/Real-valued_functions/Images/lower_sum.tex index 0738a04..8779eed 100644 --- a/Mathematics/1st/Real-valued_functions/Images/lower_sum.tex +++ b/Mathematics/1st/Real-valued_functions/Images/lower_sum.tex @@ -1,5 +1,5 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} \begin{document} \begin{tikzpicture}[ diff --git a/Mathematics/1st/Real-valued_functions/Images/upper_sum.pdf b/Mathematics/1st/Real-valued_functions/Images/upper_sum.pdf index 2c38c7b..37cf075 100644 Binary files a/Mathematics/1st/Real-valued_functions/Images/upper_sum.pdf and b/Mathematics/1st/Real-valued_functions/Images/upper_sum.pdf differ diff --git a/Mathematics/1st/Real-valued_functions/Images/upper_sum.tex b/Mathematics/1st/Real-valued_functions/Images/upper_sum.tex index 6e69137..c19ea5f 100644 --- a/Mathematics/1st/Real-valued_functions/Images/upper_sum.tex +++ b/Mathematics/1st/Real-valued_functions/Images/upper_sum.tex @@ -1,5 +1,5 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} \begin{document} \begin{tikzpicture}[ diff --git a/Mathematics/2nd/Algebraic_structures/Images/circles.pdf b/Mathematics/2nd/Algebraic_structures/Images/circles.pdf index 5318443..1e9c311 100644 Binary files a/Mathematics/2nd/Algebraic_structures/Images/circles.pdf and b/Mathematics/2nd/Algebraic_structures/Images/circles.pdf differ diff --git a/Mathematics/2nd/Algebraic_structures/Images/circles.tex b/Mathematics/2nd/Algebraic_structures/Images/circles.tex index 1092f84..04ca5d0 100644 --- a/Mathematics/2nd/Algebraic_structures/Images/circles.tex +++ b/Mathematics/2nd/Algebraic_structures/Images/circles.tex @@ -1,5 +1,6 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} +\usepackage{../../../../preamble_math} \begin{document} \begin{tikzpicture} diff --git a/Mathematics/2nd/Algebraic_structures/Images/theorem1.pdf b/Mathematics/2nd/Algebraic_structures/Images/theorem1.pdf index babd00e..11cd6dd 100644 Binary files a/Mathematics/2nd/Algebraic_structures/Images/theorem1.pdf and b/Mathematics/2nd/Algebraic_structures/Images/theorem1.pdf differ diff --git a/Mathematics/2nd/Algebraic_structures/Images/theorem1.tex b/Mathematics/2nd/Algebraic_structures/Images/theorem1.tex index 2f10357..51cdfbb 100644 --- a/Mathematics/2nd/Algebraic_structures/Images/theorem1.tex +++ b/Mathematics/2nd/Algebraic_structures/Images/theorem1.tex @@ -1,5 +1,7 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} +\usepackage{../../../../preamble_math} + \begin{document} diff --git a/Mathematics/2nd/Algebraic_structures/Images/theorem2.pdf b/Mathematics/2nd/Algebraic_structures/Images/theorem2.pdf index c4295b4..f5586ec 100644 Binary files a/Mathematics/2nd/Algebraic_structures/Images/theorem2.pdf and b/Mathematics/2nd/Algebraic_structures/Images/theorem2.pdf differ diff --git a/Mathematics/2nd/Algebraic_structures/Images/theorem2.tex b/Mathematics/2nd/Algebraic_structures/Images/theorem2.tex index c7e9227..507013a 100644 --- a/Mathematics/2nd/Algebraic_structures/Images/theorem2.tex +++ b/Mathematics/2nd/Algebraic_structures/Images/theorem2.tex @@ -1,5 +1,6 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} +\usepackage{../../../../preamble_math} \begin{document} diff --git a/Mathematics/2nd/Algebraic_structures/Images/theorem3.pdf b/Mathematics/2nd/Algebraic_structures/Images/theorem3.pdf index 2c056d6..07f46e4 100644 Binary files a/Mathematics/2nd/Algebraic_structures/Images/theorem3.pdf and b/Mathematics/2nd/Algebraic_structures/Images/theorem3.pdf differ diff --git a/Mathematics/2nd/Algebraic_structures/Images/theorem3.tex b/Mathematics/2nd/Algebraic_structures/Images/theorem3.tex index 6494105..857992b 100644 --- a/Mathematics/2nd/Algebraic_structures/Images/theorem3.tex +++ b/Mathematics/2nd/Algebraic_structures/Images/theorem3.tex @@ -1,16 +1,16 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} \begin{document} \begin{tikzpicture} - %%% NODES - \path (0,0) node(x) {$R$} - (2,0) node(y) {$S$} (0,-2) node(z) {$R[x]$}; - %%% LINES - \draw[very thin,->] (x) --node[above,midway] {$\phi$} (y); - \draw[very thin,->] (z) --node[right,pos=0.45] {$\psi$} (y); - \draw[very thin,right hook->] (x) --node[left,midway] {$i$} (z); + %%% NODES + \path (0,0) node(x) {$R$} + (2,0) node(y) {$S$} (0,-2) node(z) {$R[x]$}; + %%% LINES + \draw[very thin,->] (x) --node[above,midway] {$\phi$} (y); + \draw[very thin,->] (z) --node[right,pos=0.45] {$\psi$} (y); + \draw[very thin,right hook->] (x) --node[left,midway] {$i$} (z); \end{tikzpicture} \end{document} \ No newline at end of file diff --git a/Mathematics/2nd/Algebraic_structures/Images/theorem4.pdf b/Mathematics/2nd/Algebraic_structures/Images/theorem4.pdf index 1768bc0..9f85c15 100644 Binary files a/Mathematics/2nd/Algebraic_structures/Images/theorem4.pdf and b/Mathematics/2nd/Algebraic_structures/Images/theorem4.pdf differ diff --git a/Mathematics/2nd/Algebraic_structures/Images/theorem4.tex b/Mathematics/2nd/Algebraic_structures/Images/theorem4.tex index fe90dcc..c58c1e3 100644 --- a/Mathematics/2nd/Algebraic_structures/Images/theorem4.tex +++ b/Mathematics/2nd/Algebraic_structures/Images/theorem4.tex @@ -1,15 +1,15 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} \begin{document} \begin{tikzpicture} - %%% NODES - \path (0,0) node(x) {$R$} - (2,0) node(y) {$K$} (0,-2) node(z) {$Q(R)$}; - %%% LINES - \draw[very thin,->] (x) --node[above,midway] {$\phi$} (y); - \draw[very thin,->] (z) --node[right,pos=0.45] {$\psi$} (y); - \draw[very thin,right hook->] (x) --node[left,midway] {$i$} (z); + %%% NODES + \path (0,0) node(x) {$R$} + (2,0) node(y) {$K$} (0,-2) node(z) {$Q(R)$}; + %%% LINES + \draw[very thin,->] (x) --node[above,midway] {$\phi$} (y); + \draw[very thin,->] (z) --node[right,pos=0.45] {$\psi$} (y); + \draw[very thin,right hook->] (x) --node[left,midway] {$i$} (z); \end{tikzpicture} \end{document} \ No newline at end of file diff --git a/Mathematics/2nd/Discrete_mathematics/Images/bipartite.pdf b/Mathematics/2nd/Discrete_mathematics/Images/bipartite.pdf index 06744c8..263378d 100644 Binary files a/Mathematics/2nd/Discrete_mathematics/Images/bipartite.pdf and b/Mathematics/2nd/Discrete_mathematics/Images/bipartite.pdf differ diff --git a/Mathematics/2nd/Discrete_mathematics/Images/bipartite.tex b/Mathematics/2nd/Discrete_mathematics/Images/bipartite.tex index 85baec1..ae0804d 100644 --- a/Mathematics/2nd/Discrete_mathematics/Images/bipartite.tex +++ b/Mathematics/2nd/Discrete_mathematics/Images/bipartite.tex @@ -1,5 +1,6 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_general} +\usepackage{../../../../preamble_tikz} \begin{document} \begin{tikzpicture} diff --git a/Mathematics/2nd/Discrete_mathematics/Images/complete5.pdf b/Mathematics/2nd/Discrete_mathematics/Images/complete5.pdf index a6e8662..c2d9346 100644 Binary files a/Mathematics/2nd/Discrete_mathematics/Images/complete5.pdf and b/Mathematics/2nd/Discrete_mathematics/Images/complete5.pdf differ diff --git a/Mathematics/2nd/Discrete_mathematics/Images/complete5.tex b/Mathematics/2nd/Discrete_mathematics/Images/complete5.tex index 1ae7bb1..a80082c 100644 --- a/Mathematics/2nd/Discrete_mathematics/Images/complete5.tex +++ b/Mathematics/2nd/Discrete_mathematics/Images/complete5.tex @@ -1,5 +1,5 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} \begin{document} \begin{tikzpicture} diff --git a/Mathematics/2nd/Discrete_mathematics/Images/graph.pdf b/Mathematics/2nd/Discrete_mathematics/Images/graph.pdf index d0dde9f..b8b363f 100644 Binary files a/Mathematics/2nd/Discrete_mathematics/Images/graph.pdf and b/Mathematics/2nd/Discrete_mathematics/Images/graph.pdf differ diff --git a/Mathematics/2nd/Discrete_mathematics/Images/graph.tex b/Mathematics/2nd/Discrete_mathematics/Images/graph.tex index 6a16390..d49de98 100644 --- a/Mathematics/2nd/Discrete_mathematics/Images/graph.tex +++ b/Mathematics/2nd/Discrete_mathematics/Images/graph.tex @@ -1,5 +1,5 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} \begin{document} \begin{tikzpicture} diff --git a/Mathematics/2nd/Discrete_mathematics/Images/tree.pdf b/Mathematics/2nd/Discrete_mathematics/Images/tree.pdf index 24bbbb7..1dc4ea9 100644 Binary files a/Mathematics/2nd/Discrete_mathematics/Images/tree.pdf and b/Mathematics/2nd/Discrete_mathematics/Images/tree.pdf differ diff --git a/Mathematics/2nd/Discrete_mathematics/Images/tree.tex b/Mathematics/2nd/Discrete_mathematics/Images/tree.tex index 4d29489..a2044e7 100644 --- a/Mathematics/2nd/Discrete_mathematics/Images/tree.tex +++ b/Mathematics/2nd/Discrete_mathematics/Images/tree.tex @@ -1,5 +1,5 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} \begin{document} \begin{tikzpicture} diff --git a/Mathematics/2nd/Linear_geometry/Images/desargues.pdf b/Mathematics/2nd/Linear_geometry/Images/desargues.pdf index 5b0e083..244e302 100644 Binary files a/Mathematics/2nd/Linear_geometry/Images/desargues.pdf and b/Mathematics/2nd/Linear_geometry/Images/desargues.pdf differ diff --git a/Mathematics/2nd/Linear_geometry/Images/desargues.tex b/Mathematics/2nd/Linear_geometry/Images/desargues.tex index 960adf5..24bc146 100644 --- a/Mathematics/2nd/Linear_geometry/Images/desargues.tex +++ b/Mathematics/2nd/Linear_geometry/Images/desargues.tex @@ -1,43 +1,43 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} \begin{document} \begin{tikzpicture} - %%% LINES - \draw[color=red!80, thin] (-2.14,-3) -- (4.29,-3); - \draw[color=blue!80, dotted, very thick] (-2.14,0) -- (4.3,0); - \draw[color=blue!80, dotted, very thick] (-2.14,1.71) -- (4.3,-0.43); - \draw[color=blue!80, dotted, very thick] (-2.14,2.57) -- (4.3,-0.65); - \draw[color=gray, thin] (-2.05,-3.1) -- (1.07,3.14); - \draw[color=gray, thin] (-2.1,-3.1) -- (4.14,3.14); - \draw[color=gray, thin] (0.28,-3.1) -- (-1.29,3.14); - \draw[color=gray, thin] (0.22,-3.1) -- (1.78,3.14); - \draw[color=gray, thin] (4.07,-3.1) -- (-0.38,3.14); - \draw[color=gray, thin] (4.1,-3.1) -- (-2.14,3.14); + %%% LINES + \draw[color=red!80, thin] (-2.14,-3) -- (4.29,-3); + \draw[color=blue!80, dotted, very thick] (-2.14,0) -- (4.3,0); + \draw[color=blue!80, dotted, very thick] (-2.14,1.71) -- (4.3,-0.43); + \draw[color=blue!80, dotted, very thick] (-2.14,2.57) -- (4.3,-0.65); + \draw[color=gray, thin] (-2.05,-3.1) -- (1.07,3.14); + \draw[color=gray, thin] (-2.1,-3.1) -- (4.14,3.14); + \draw[color=gray, thin] (0.28,-3.1) -- (-1.29,3.14); + \draw[color=gray, thin] (0.22,-3.1) -- (1.78,3.14); + \draw[color=gray, thin] (4.07,-3.1) -- (-0.38,3.14); + \draw[color=gray, thin] (4.1,-3.1) -- (-2.14,3.14); - %%% TRIANGLES - \filldraw[fill=black!50!green!50, thin] (-0.5,0) -- (0,1) -- (-1,2) -- cycle; - \filldraw[fill=black!10!yellow!60, thin] (1,0) -- (1.5,0.5) -- (1.22,0.89) -- cycle; + %%% TRIANGLES + \filldraw[fill=black!50!green!50, thin] (-0.5,0) -- (0,1) -- (-1,2) -- cycle; + \filldraw[fill=black!10!yellow!60, thin] (1,0) -- (1.5,0.5) -- (1.22,0.89) -- cycle; - %%% POINTS - %% TRIANGLES - \filldraw[red!80] (-0.5,0) circle (0.7pt); - \filldraw[red!80] (0,1) circle (0.7pt); - \filldraw[red!80] (-1,2) circle (0.7pt); - \filldraw[red!80] (1,0) circle (0.7pt); - \filldraw[red!80] (1.5,0.5) circle (0.7pt); - \filldraw[red!80] (1.22,0.89) circle (0.7pt); + %%% POINTS + %% TRIANGLES + \filldraw[red!80] (-0.5,0) circle (0.7pt); + \filldraw[red!80] (0,1) circle (0.7pt); + \filldraw[red!80] (-1,2) circle (0.7pt); + \filldraw[red!80] (1,0) circle (0.7pt); + \filldraw[red!80] (1.5,0.5) circle (0.7pt); + \filldraw[red!80] (1.22,0.89) circle (0.7pt); - %% INTERSECTIONS - \filldraw[red!80] (3,0) circle (0.7pt); - \filldraw[red!80] (-2,-3) circle (0.7pt); - \filldraw[red!80] (0.25,-3) circle (0.7pt); - \filldraw[red!80] (4,-3) circle (0.7pt); + %% INTERSECTIONS + \filldraw[red!80] (3,0) circle (0.7pt); + \filldraw[red!80] (-2,-3) circle (0.7pt); + \filldraw[red!80] (0.25,-3) circle (0.7pt); + \filldraw[red!80] (4,-3) circle (0.7pt); - %%% WORDS - \node[scale=0.5,align=center] at (3.3,0.4) {Center of\\perspectivity}; - \node[scale=0.5,align=center] at (2,-2.87) {Axis of perspectivity}; + %%% WORDS + \node[scale=0.5,align=center] at (3.3,0.4) {Center of\\perspectivity}; + \node[scale=0.5,align=center] at (2,-2.87) {Axis of perspectivity}; \end{tikzpicture} \end{document} \ No newline at end of file diff --git a/Mathematics/2nd/Linear_geometry/Images/disk.pdf b/Mathematics/2nd/Linear_geometry/Images/disk.pdf index 4bdd813..d6f9265 100644 Binary files a/Mathematics/2nd/Linear_geometry/Images/disk.pdf and b/Mathematics/2nd/Linear_geometry/Images/disk.pdf differ diff --git a/Mathematics/2nd/Linear_geometry/Images/disk.tex b/Mathematics/2nd/Linear_geometry/Images/disk.tex index 662552b..a349250 100644 --- a/Mathematics/2nd/Linear_geometry/Images/disk.tex +++ b/Mathematics/2nd/Linear_geometry/Images/disk.tex @@ -1,35 +1,43 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} \begin{document} \begin{tikzpicture}[scale=2] - \tkzDefPoint(0,0){O} - \tkzDefPoint(0,1){P} - \tkzDefPoint(-1,0){M} - \tkzDefPoint(1,0){N} - \tkzDefPoint(-0.73,0.683){A} - \tkzDefPoint(0.929,0.38){B} - \tkzDefPoint(0.978,-0.209){C} - \tkzDefPoint(-0.939,0.344){D} - \tkzDefPoint(-0.223,0.975){E} - \tkzDefPoint(-0.589,-0.808){F} - \tkzDefPoint(0.395,0.919){G} - \tkzDefPoint(0.596,-0.803){H} - \tkzDefPoint(-0.972,-0.234){I} - \tkzDefPoint(-0.768,-0.641){J} - \tkzDefPoint(-0.053,-0.999){K} - %%% LINES - \tkzDrawCircle(O,A) - \tkzClipCircle(O,A) % only print hyperbolic lines inside the unit circle. - \tkzDrawCircle[orthogonal through=A and B](O,P) - \tkzDrawCircle[orthogonal through=C and B](O,P) - \tkzDrawCircle[orthogonal through=C and D](O,P) - \tkzDrawCircle[orthogonal through=E and F](O,P) - \tkzDrawCircle[orthogonal through=G and H](O,P) - \tkzDrawCircle[orthogonal through=I and J](O,P) - \tkzDrawCircle[orthogonal through=I and K](O,P) - \draw[semithick] (-1,0) -- (1,0); + \tkzDefPoint(0,0){O} + \tkzDefPoint(0,1){P} + \tkzDefPoint(-1,0){M} + \tkzDefPoint(1,0){N} + \tkzDefPoint(-0.73,0.683){A} + \tkzDefPoint(0.929,0.38){B} + \tkzDefPoint(0.978,-0.209){C} + \tkzDefPoint(-0.939,0.344){D} + \tkzDefPoint(-0.223,0.975){E} + \tkzDefPoint(-0.589,-0.808){F} + \tkzDefPoint(0.395,0.919){G} + \tkzDefPoint(0.596,-0.803){H} + \tkzDefPoint(-0.972,-0.234){I} + \tkzDefPoint(-0.768,-0.641){J} + \tkzDefPoint(-0.053,-0.999){K} + %%% LINES + \tkzDrawCircle[thick, black](O,A) + \tkzClipCircle(O,A) % only print hyperbolic lines inside the unit circle. + \tkzDefCircle[orthogonal through=A and B](O,P) \tkzGetPoints{a}{b} + \tkzDrawCircle[semithick,black](a,b) + \tkzDefCircle[orthogonal through=C and B](O,P) \tkzGetPoints{c}{d} + \tkzDrawCircle[semithick,black](c,d) + \tkzDefCircle[orthogonal through=C and D](O,P) \tkzGetPoints{e}{f} + \tkzDrawCircle[semithick,black](e,f) + \tkzDefCircle[orthogonal through=E and F](O,P) \tkzGetPoints{g}{h} + \tkzDrawCircle[semithick,black](g,h) + \tkzDefCircle[orthogonal through=G and H](O,P) \tkzGetPoints{i}{j} + \tkzDrawCircle[semithick,black](i,j) + \tkzDefCircle[orthogonal through=I and J](O,P) \tkzGetPoints{k}{l} + \tkzDrawCircle[semithick,black](k,l) + \tkzDefCircle[orthogonal through=I and K](O,P) \tkzGetPoints{m}{n} + \tkzDrawCircle[semithick,black](m,n) + + \draw[semithick,black] (M) -- (N); \end{tikzpicture} \end{document} \ No newline at end of file diff --git a/Mathematics/2nd/Linear_geometry/Images/fano.pdf b/Mathematics/2nd/Linear_geometry/Images/fano.pdf index 481433d..94c9f9b 100644 Binary files a/Mathematics/2nd/Linear_geometry/Images/fano.pdf and b/Mathematics/2nd/Linear_geometry/Images/fano.pdf differ diff --git a/Mathematics/2nd/Linear_geometry/Images/fano.tex b/Mathematics/2nd/Linear_geometry/Images/fano.tex index 0cbbcda..529b75a 100644 --- a/Mathematics/2nd/Linear_geometry/Images/fano.tex +++ b/Mathematics/2nd/Linear_geometry/Images/fano.tex @@ -1,25 +1,25 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} \begin{document} \begin{tikzpicture} - %%% LINES - \draw[very thin] (0,0) -- (1,0); - \draw[very thin] (0.5,0.87) -- (1,0); - \draw[very thin] (0,0) -- (0.5,0.87); - \draw[very thin] (0.5,0) -- (0.5,0.87); - \draw[very thin] (1,0) -- (0.25,0.43); - \draw[very thin] (0,0) -- (0.75,0.43); - \draw[very thin] (0.5,0.29) circle (0.29); - %%% POINTS - \filldraw[red!80] (0,0) circle (0.5pt); - \filldraw[red!80] (0.5,0) circle (0.5pt); - \filldraw[red!80] (1,0) circle (0.5pt); - \filldraw[red!80] (0.75,0.43) circle (0.5pt); - \filldraw[red!80] (0.5,0.87) circle (0.5pt); - \filldraw[red!80] (0.25,0.43) circle (0.5pt); - \filldraw[red!80] (0.5,0.29) circle (0.5pt); + %%% LINES + \draw[very thin] (0,0) -- (1,0); + \draw[very thin] (0.5,0.87) -- (1,0); + \draw[very thin] (0,0) -- (0.5,0.87); + \draw[very thin] (0.5,0) -- (0.5,0.87); + \draw[very thin] (1,0) -- (0.25,0.43); + \draw[very thin] (0,0) -- (0.75,0.43); + \draw[very thin] (0.5,0.29) circle (0.29); + %%% POINTS + \filldraw[red!80] (0,0) circle (0.5pt); + \filldraw[red!80] (0.5,0) circle (0.5pt); + \filldraw[red!80] (1,0) circle (0.5pt); + \filldraw[red!80] (0.75,0.43) circle (0.5pt); + \filldraw[red!80] (0.5,0.87) circle (0.5pt); + \filldraw[red!80] (0.25,0.43) circle (0.5pt); + \filldraw[red!80] (0.5,0.29) circle (0.5pt); \end{tikzpicture} \end{document} \ No newline at end of file diff --git a/Mathematics/2nd/Linear_geometry/Images/half.pdf b/Mathematics/2nd/Linear_geometry/Images/half.pdf index 681b9e6..ac142b8 100644 Binary files a/Mathematics/2nd/Linear_geometry/Images/half.pdf and b/Mathematics/2nd/Linear_geometry/Images/half.pdf differ diff --git a/Mathematics/2nd/Linear_geometry/Images/half.tex b/Mathematics/2nd/Linear_geometry/Images/half.tex index 43deca0..e9b00a0 100644 --- a/Mathematics/2nd/Linear_geometry/Images/half.tex +++ b/Mathematics/2nd/Linear_geometry/Images/half.tex @@ -1,18 +1,18 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} \begin{document} \begin{tikzpicture} - %%% LINES - \draw[very thin] (-2,0) -- (2,0); - \draw[very thin] (0,0) -- (0,2); - \draw[very thin] (1.5,0) -- (1.5,2); - \draw[very thin] (-1.1,0) -- (-1.1,2); - %%% CIRCLES - \draw[very thin] (1.5,0) arc (0:180:1.25); - \draw[very thin] (1.5,0) arc (0:180:0.25); - \draw[very thin] (-0.25,0) arc (0:180:0.75); + %%% LINES + \draw[very thin] (-2,0) -- (2,0); + \draw[very thin] (0,0) -- (0,2); + \draw[very thin] (1.5,0) -- (1.5,2); + \draw[very thin] (-1.1,0) -- (-1.1,2); + %%% CIRCLES + \draw[very thin] (1.5,0) arc (0:180:1.25); + \draw[very thin] (1.5,0) arc (0:180:0.25); + \draw[very thin] (-0.25,0) arc (0:180:0.75); \end{tikzpicture} \end{document} \ No newline at end of file diff --git a/Mathematics/2nd/Linear_geometry/Images/klein.pdf b/Mathematics/2nd/Linear_geometry/Images/klein.pdf index acca333..e6dd95c 100644 Binary files a/Mathematics/2nd/Linear_geometry/Images/klein.pdf and b/Mathematics/2nd/Linear_geometry/Images/klein.pdf differ diff --git a/Mathematics/2nd/Linear_geometry/Images/klein.tex b/Mathematics/2nd/Linear_geometry/Images/klein.tex index ff3d2ef..d0fcb15 100644 --- a/Mathematics/2nd/Linear_geometry/Images/klein.tex +++ b/Mathematics/2nd/Linear_geometry/Images/klein.tex @@ -1,19 +1,19 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} \begin{document} \begin{tikzpicture} - %%% LINES - \draw[very thin] (0,1) -- (0,-1); - \draw[very thin] (-0.394,0.919) -- (1,0); - \draw[very thin] (-0.87,0.493) -- (0.922,0.388); - \draw[very thin] (-0.991,0.13) -- (0.851,0.525); - \draw[very thin] (-0.968,-0.25) -- (0.777,0.63); - \draw[very thin] (0.664,0.748) -- (0.09,-0.996); + %%% LINES + \draw[very thin] (0,1) -- (0,-1); + \draw[very thin] (-0.394,0.919) -- (1,0); + \draw[very thin] (-0.87,0.493) -- (0.922,0.388); + \draw[very thin] (-0.991,0.13) -- (0.851,0.525); + \draw[very thin] (-0.968,-0.25) -- (0.777,0.63); + \draw[very thin] (0.664,0.748) -- (0.09,-0.996); - %%% CIRCLE - \draw[very thin] (0,0) circle (1); + %%% CIRCLE + \draw[very thin] (0,0) circle (1); \end{tikzpicture} \end{document} \ No newline at end of file diff --git a/Mathematics/2nd/Linear_geometry/Images/pappus.pdf b/Mathematics/2nd/Linear_geometry/Images/pappus.pdf index 47a00be..949b04d 100644 Binary files a/Mathematics/2nd/Linear_geometry/Images/pappus.pdf and b/Mathematics/2nd/Linear_geometry/Images/pappus.pdf differ diff --git a/Mathematics/2nd/Linear_geometry/Images/pappus.tex b/Mathematics/2nd/Linear_geometry/Images/pappus.tex index 83fc875..d45c4a1 100644 --- a/Mathematics/2nd/Linear_geometry/Images/pappus.tex +++ b/Mathematics/2nd/Linear_geometry/Images/pappus.tex @@ -1,29 +1,29 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} \begin{document} \begin{tikzpicture} - %%% LINES - \draw[very thin] (0,0) -- (1,0); - \draw[very thin] (0.5,1) -- (1,0); - \draw[very thin] (0,0) -- (0.5,1); - \draw[very thin] (0,1) -- (0.5,0); - \draw[very thin] (1,1) -- (0.5,0); - \draw[very thin] (0,1) -- (1,1); - \draw[very thin] (0,0) -- (1,1); - \draw[very thin] (0,1) -- (1,0); - \draw[very thin] (0.25,0.5) -- (0.75,0.5); - %%% POINTS - \filldraw[red!80] (0,0) circle (0.5pt); - \filldraw[red!80] (0.5,0) circle (0.5pt); - \filldraw[red!80] (1,0) circle (0.5pt); - \filldraw[red!80] (0,1) circle (0.5pt); - \filldraw[red!80] (0.5,1) circle (0.5pt); - \filldraw[red!80] (1,1) circle (0.5pt); - \filldraw[red!80] (0.25,0.5) circle (0.5pt); - \filldraw[red!80] (0.5,0.5) circle (0.5pt); - \filldraw[red!80] (0.75,0.5) circle (0.5pt); + %%% LINES + \draw[very thin] (0,0) -- (1,0); + \draw[very thin] (0.5,1) -- (1,0); + \draw[very thin] (0,0) -- (0.5,1); + \draw[very thin] (0,1) -- (0.5,0); + \draw[very thin] (1,1) -- (0.5,0); + \draw[very thin] (0,1) -- (1,1); + \draw[very thin] (0,0) -- (1,1); + \draw[very thin] (0,1) -- (1,0); + \draw[very thin] (0.25,0.5) -- (0.75,0.5); + %%% POINTS + \filldraw[red!80] (0,0) circle (0.5pt); + \filldraw[red!80] (0.5,0) circle (0.5pt); + \filldraw[red!80] (1,0) circle (0.5pt); + \filldraw[red!80] (0,1) circle (0.5pt); + \filldraw[red!80] (0.5,1) circle (0.5pt); + \filldraw[red!80] (1,1) circle (0.5pt); + \filldraw[red!80] (0.25,0.5) circle (0.5pt); + \filldraw[red!80] (0.5,0.5) circle (0.5pt); + \filldraw[red!80] (0.75,0.5) circle (0.5pt); \end{tikzpicture} \end{document} \ No newline at end of file diff --git a/Mathematics/2nd/Numerical_methods/Images/cobweb1.pdf b/Mathematics/2nd/Numerical_methods/Images/cobweb1.pdf index c29ff63..3cf82a6 100644 Binary files a/Mathematics/2nd/Numerical_methods/Images/cobweb1.pdf and b/Mathematics/2nd/Numerical_methods/Images/cobweb1.pdf differ diff --git a/Mathematics/2nd/Numerical_methods/Images/cobweb1.tex b/Mathematics/2nd/Numerical_methods/Images/cobweb1.tex index 2d6c1a6..fb1da28 100644 --- a/Mathematics/2nd/Numerical_methods/Images/cobweb1.tex +++ b/Mathematics/2nd/Numerical_methods/Images/cobweb1.tex @@ -1,5 +1,5 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} \begin{document} \pgfkeys{/pgf/declare function={f(\x)=cos(deg(\x));}} % Here you can declare multivariable functions like this: @@ -11,23 +11,23 @@ % speech(\t) = 1 + source(\t)*filter(\t); % } \begin{tikzpicture} - \begin{axis}[xmin = 0, xmax = 1.2,ymin = 0, ymax = 1.2, axis equal image] - \addplot [thin,samples=200,smooth,blue] {f(x)}; - \addplot [thin,samples=200,smooth,black] {x}; - \pgfplotsextra{ - \def\x{0.125} - \def\y{0} - \draw [very thin,red] (axis cs:\x,\y) \foreach \i in {0,...,16}{ - \pgfextra{ - \pgfkeys{/pgf/fpu=true, /pgf/fpu/output format=fixed} - \pgfmathparse{f(\x)}\xdef\y{\pgfmathresult} - } - -- (axis cs:\x,\y) - \pgfextra{\xdef\x{\y}} - -- (axis cs:{\x},{\y}) - };} - \draw [thin,color_green2,dashed] (axis cs:0.739,0) -- node[left,pos=0.05]{$\alpha$} (axis cs:0.739,0.739); - \legend{$g(x)$} - \end{axis} + \begin{axis}[xmin = 0, xmax = 1.2,ymin = 0, ymax = 1.2, axis equal image] + \addplot [thin,samples=200,smooth,blue] {f(x)}; + \addplot [thin,samples=200,smooth,black] {x}; + \pgfplotsextra{ + \def\x{0.125} + \def\y{0} + \draw [very thin,red] (axis cs:\x,\y) \foreach \i in {0,...,16}{ + \pgfextra{ + \pgfkeys{/pgf/fpu=true, /pgf/fpu/output format=fixed} + \pgfmathparse{f(\x)}\xdef\y{\pgfmathresult} + } + -- (axis cs:\x,\y) + \pgfextra{\xdef\x{\y}} + -- (axis cs:{\x},{\y}) + };} + \draw [thin,color_green2,dashed] (axis cs:0.739,0) -- node[left,pos=0.05]{$\alpha$} (axis cs:0.739,0.739); + \legend{$g(x)$} + \end{axis} \end{tikzpicture} \end{document} \ No newline at end of file diff --git a/Mathematics/2nd/Numerical_methods/Images/cobweb2.pdf b/Mathematics/2nd/Numerical_methods/Images/cobweb2.pdf index fc146a8..569b77c 100644 Binary files a/Mathematics/2nd/Numerical_methods/Images/cobweb2.pdf and b/Mathematics/2nd/Numerical_methods/Images/cobweb2.pdf differ diff --git a/Mathematics/2nd/Numerical_methods/Images/cobweb2.tex b/Mathematics/2nd/Numerical_methods/Images/cobweb2.tex index 618cd8b..e1a691f 100644 --- a/Mathematics/2nd/Numerical_methods/Images/cobweb2.tex +++ b/Mathematics/2nd/Numerical_methods/Images/cobweb2.tex @@ -1,5 +1,5 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} \begin{document} \pgfkeys{/pgf/declare function={f(\x)=1.65*\x*(1-0.4*\x);}} % Here you can declare multivariable functions to like this: @@ -11,24 +11,24 @@ % speech(\t) = 1 + source(\t)*filter(\t); % } \begin{tikzpicture} - \begin{axis}[xmin=0,xmax=1.2,ymin=0,ymax=1.2, - axis equal image] - \addplot [thin,samples=200,smooth,blue] {f(x)}; - \addplot [thin,samples=200,smooth,black] {x}; - \pgfplotsextra{ - \def\x{0.2} - \def\y{0} - \draw [very thin,red] (axis cs:\x,\y) \foreach \i in {0,...,10}{ - \pgfextra{ - \pgfkeys{/pgf/fpu=true, /pgf/fpu/output format=fixed} - \pgfmathparse{f(\x)}\xdef\y{\pgfmathresult} - } - -- (axis cs:\x,\y) - \pgfextra{\xdef\x{\y}} - -- (axis cs:{\x},{\y}) - };} - \draw [thin,color_green2,dashed] (axis cs:0.985,0) -- node[left,pos=0.05]{$\alpha$} (axis cs:0.985,0.985); - \legend{$g(x)$} - \end{axis} + \begin{axis}[xmin=0,xmax=1.2,ymin=0,ymax=1.2, + axis equal image] + \addplot [thin,samples=200,smooth,blue] {f(x)}; + \addplot [thin,samples=200,smooth,black] {x}; + \pgfplotsextra{ + \def\x{0.2} + \def\y{0} + \draw [very thin,red] (axis cs:\x,\y) \foreach \i in {0,...,10}{ + \pgfextra{ + \pgfkeys{/pgf/fpu=true, /pgf/fpu/output format=fixed} + \pgfmathparse{f(\x)}\xdef\y{\pgfmathresult} + } + -- (axis cs:\x,\y) + \pgfextra{\xdef\x{\y}} + -- (axis cs:{\x},{\y}) + };} + \draw [thin,color_green2,dashed] (axis cs:0.985,0) -- node[left,pos=0.05]{$\alpha$} (axis cs:0.985,0.985); + \legend{$g(x)$} + \end{axis} \end{tikzpicture} \end{document} \ No newline at end of file diff --git a/Mathematics/2nd/Numerical_methods/Images/cobweb3.pdf b/Mathematics/2nd/Numerical_methods/Images/cobweb3.pdf index 403140d..81fd0df 100644 Binary files a/Mathematics/2nd/Numerical_methods/Images/cobweb3.pdf and b/Mathematics/2nd/Numerical_methods/Images/cobweb3.pdf differ diff --git a/Mathematics/2nd/Numerical_methods/Images/cobweb3.tex b/Mathematics/2nd/Numerical_methods/Images/cobweb3.tex index 821fa0d..6a42975 100644 --- a/Mathematics/2nd/Numerical_methods/Images/cobweb3.tex +++ b/Mathematics/2nd/Numerical_methods/Images/cobweb3.tex @@ -1,5 +1,5 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} \begin{document} \pgfkeys{/pgf/declare function={f(\x)=1.65*\x-0.3;}} % Here you can declare multivariable functions to like this: @@ -11,37 +11,37 @@ % speech(\t) = 1 + source(\t)*filter(\t); % } \begin{tikzpicture} - \begin{axis}[xmin=0,xmax=1.2,ymin=0,ymax=1.2,axis equal image] - \addplot [thin,samples=200,smooth,blue] {f(x)}; - \addplot [thin,samples=200,smooth,black] {x}; - %%%%% Red lines 1 - \pgfplotsextra{ - \def\x{0.44} - \def\y{0} - \draw [very thin,red] (axis cs:\x,\y) \foreach \i in {0,...,6}{ - \pgfextra{ - \pgfkeys{/pgf/fpu=true, /pgf/fpu/output format=fixed} - \pgfmathparse{f(\x)}\xdef\y{\pgfmathresult} - } - -- (axis cs:\x,\y) - \pgfextra{\xdef\x{\y}} - -- (axis cs:{\x},{\y}) - };} - %%%%% Red lines 2 - \pgfplotsextra{ - \def\x{0.48} - \def\y{0} - \draw [very thin,red] (axis cs:\x,\y) \foreach \i in {0,...,7}{ - \pgfextra{ - \pgfkeys{/pgf/fpu=true, /pgf/fpu/output format=fixed} - \pgfmathparse{f(\x)}\xdef\y{\pgfmathresult} - } - -- (axis cs:\x,\y) - \pgfextra{\xdef\x{\y}} - -- (axis cs:{\x},{\y}) - };} - \draw [thin,color_green2,dashed] (axis cs:0.4615,0) -- node[left,pos=0.1]{$\alpha$} (axis cs:0.4615,0.4615); - \legend{$g(x)$} - \end{axis} + \begin{axis}[xmin=0,xmax=1.2,ymin=0,ymax=1.2,axis equal image] + \addplot [thin,samples=200,smooth,blue] {f(x)}; + \addplot [thin,samples=200,smooth,black] {x}; + %%%%% Red lines 1 + \pgfplotsextra{ + \def\x{0.44} + \def\y{0} + \draw [very thin,red] (axis cs:\x,\y) \foreach \i in {0,...,6}{ + \pgfextra{ + \pgfkeys{/pgf/fpu=true, /pgf/fpu/output format=fixed} + \pgfmathparse{f(\x)}\xdef\y{\pgfmathresult} + } + -- (axis cs:\x,\y) + \pgfextra{\xdef\x{\y}} + -- (axis cs:{\x},{\y}) + };} + %%%%% Red lines 2 + \pgfplotsextra{ + \def\x{0.48} + \def\y{0} + \draw [very thin,red] (axis cs:\x,\y) \foreach \i in {0,...,7}{ + \pgfextra{ + \pgfkeys{/pgf/fpu=true, /pgf/fpu/output format=fixed} + \pgfmathparse{f(\x)}\xdef\y{\pgfmathresult} + } + -- (axis cs:\x,\y) + \pgfextra{\xdef\x{\y}} + -- (axis cs:{\x},{\y}) + };} + \draw [thin,color_green2,dashed] (axis cs:0.4615,0) -- node[left,pos=0.1]{$\alpha$} (axis cs:0.4615,0.4615); + \legend{$g(x)$} + \end{axis} \end{tikzpicture} \end{document} \ No newline at end of file diff --git a/Mathematics/2nd/Numerical_methods/Images/cobweb4.pdf b/Mathematics/2nd/Numerical_methods/Images/cobweb4.pdf index 55c2741..1815436 100644 Binary files a/Mathematics/2nd/Numerical_methods/Images/cobweb4.pdf and b/Mathematics/2nd/Numerical_methods/Images/cobweb4.pdf differ diff --git a/Mathematics/2nd/Numerical_methods/Images/cobweb4.tex b/Mathematics/2nd/Numerical_methods/Images/cobweb4.tex index 90cde55..a1a05a1 100644 --- a/Mathematics/2nd/Numerical_methods/Images/cobweb4.tex +++ b/Mathematics/2nd/Numerical_methods/Images/cobweb4.tex @@ -1,5 +1,5 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} \begin{document} \pgfkeys{/pgf/declare function={f(\x)=3.75*\x*(1-\x);}} % Here you can declare multivariable functions to like this: @@ -11,24 +11,24 @@ % speech(\t) = 1 + source(\t)*filter(\t); % } \begin{tikzpicture} - \begin{axis}[xmin=0,xmax=1.2,ymin=0,ymax=1.2, - axis equal image] - \addplot [thin,samples=200,smooth,blue] {f(x)}; - \addplot [thin,samples=200,smooth,black] {x}; - \pgfplotsextra{ - \def\x{0.125} - \def\y{0} - \draw [very thin,red] (axis cs:\x,\y) \foreach \i in {0,...,50}{ - \pgfextra{ - \pgfkeys{/pgf/fpu=true, /pgf/fpu/output format=fixed} - \pgfmathparse{f(\x)}\xdef\y{\pgfmathresult} - } - -- (axis cs:\x,\y) - \pgfextra{\xdef\x{\y}} - -- (axis cs:{\x},{\y}) - };} - \draw [thin,color_green2,dashed] (axis cs:0.733,0) -- node[left,pos=0.05]{$\alpha$} (axis cs:0.733,0.733); - \legend{$g(x)$} - \end{axis} + \begin{axis}[xmin=0,xmax=1.2,ymin=0,ymax=1.2, + axis equal image] + \addplot [thin,samples=200,smooth,blue] {f(x)}; + \addplot [thin,samples=200,smooth,black] {x}; + \pgfplotsextra{ + \def\x{0.125} + \def\y{0} + \draw [very thin,red] (axis cs:\x,\y) \foreach \i in {0,...,50}{ + \pgfextra{ + \pgfkeys{/pgf/fpu=true, /pgf/fpu/output format=fixed} + \pgfmathparse{f(\x)}\xdef\y{\pgfmathresult} + } + -- (axis cs:\x,\y) + \pgfextra{\xdef\x{\y}} + -- (axis cs:{\x},{\y}) + };} + \draw [thin,color_green2,dashed] (axis cs:0.733,0) -- node[left,pos=0.05]{$\alpha$} (axis cs:0.733,0.733); + \legend{$g(x)$} + \end{axis} \end{tikzpicture} \end{document} \ No newline at end of file diff --git a/Mathematics/2nd/Numerical_methods/Images/runge.pdf b/Mathematics/2nd/Numerical_methods/Images/runge.pdf index 70a70e3..c3bf03a 100644 Binary files a/Mathematics/2nd/Numerical_methods/Images/runge.pdf and b/Mathematics/2nd/Numerical_methods/Images/runge.pdf differ diff --git a/Mathematics/2nd/Numerical_methods/Images/runge.tex b/Mathematics/2nd/Numerical_methods/Images/runge.tex index 93f110a..984dd81 100644 --- a/Mathematics/2nd/Numerical_methods/Images/runge.tex +++ b/Mathematics/2nd/Numerical_methods/Images/runge.tex @@ -1,5 +1,5 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} \begin{document} \begin{tikzpicture} diff --git a/Mathematics/3rd/Complex_analysis/Images/stereo.pdf b/Mathematics/3rd/Complex_analysis/Images/stereo.pdf index b446922..867958a 100644 Binary files a/Mathematics/3rd/Complex_analysis/Images/stereo.pdf and b/Mathematics/3rd/Complex_analysis/Images/stereo.pdf differ diff --git a/Mathematics/3rd/Complex_analysis/Images/stereo.tex b/Mathematics/3rd/Complex_analysis/Images/stereo.tex index 6f9caba..ca362c5 100644 --- a/Mathematics/3rd/Complex_analysis/Images/stereo.tex +++ b/Mathematics/3rd/Complex_analysis/Images/stereo.tex @@ -1,5 +1,8 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_general} +\usepackage{../../../../preamble_tikz} +\usepackage{../../../../preamble_math} + \begin{document} \begin{tikzpicture} diff --git a/Mathematics/3rd/Differential_equations/Images/apsector.pdf b/Mathematics/3rd/Differential_equations/Images/apsector.pdf index 45faac1..7cf8c8f 100644 Binary files a/Mathematics/3rd/Differential_equations/Images/apsector.pdf and b/Mathematics/3rd/Differential_equations/Images/apsector.pdf differ diff --git a/Mathematics/3rd/Differential_equations/Images/apsector.tex b/Mathematics/3rd/Differential_equations/Images/apsector.tex index a63c421..7679a07 100644 --- a/Mathematics/3rd/Differential_equations/Images/apsector.tex +++ b/Mathematics/3rd/Differential_equations/Images/apsector.tex @@ -1,5 +1,5 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} \begin{document} \begin{tikzpicture}[,decorated separatrices/.style={ diff --git a/Mathematics/3rd/Differential_equations/Images/esector.pdf b/Mathematics/3rd/Differential_equations/Images/esector.pdf index fbb8811..32290cf 100644 Binary files a/Mathematics/3rd/Differential_equations/Images/esector.pdf and b/Mathematics/3rd/Differential_equations/Images/esector.pdf differ diff --git a/Mathematics/3rd/Differential_equations/Images/esector.tex b/Mathematics/3rd/Differential_equations/Images/esector.tex index f83bfc6..0ab699a 100644 --- a/Mathematics/3rd/Differential_equations/Images/esector.tex +++ b/Mathematics/3rd/Differential_equations/Images/esector.tex @@ -1,5 +1,5 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} \begin{document} \begin{tikzpicture}[decorated curves/.style={ diff --git a/Mathematics/3rd/Differential_equations/Images/homo_hetero.pdf b/Mathematics/3rd/Differential_equations/Images/homo_hetero.pdf index de3d901..93845e3 100644 Binary files a/Mathematics/3rd/Differential_equations/Images/homo_hetero.pdf and b/Mathematics/3rd/Differential_equations/Images/homo_hetero.pdf differ diff --git a/Mathematics/3rd/Differential_equations/Images/homo_hetero.tex b/Mathematics/3rd/Differential_equations/Images/homo_hetero.tex index b9705d3..046ce6d 100644 --- a/Mathematics/3rd/Differential_equations/Images/homo_hetero.tex +++ b/Mathematics/3rd/Differential_equations/Images/homo_hetero.tex @@ -1,5 +1,5 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} %%%% Differential system %%%%% \def\xdot{y} diff --git a/Mathematics/3rd/Differential_equations/Images/hsector.pdf b/Mathematics/3rd/Differential_equations/Images/hsector.pdf index 3e1acd1..8567588 100644 Binary files a/Mathematics/3rd/Differential_equations/Images/hsector.pdf and b/Mathematics/3rd/Differential_equations/Images/hsector.pdf differ diff --git a/Mathematics/3rd/Differential_equations/Images/hsector.tex b/Mathematics/3rd/Differential_equations/Images/hsector.tex index 40c403f..7b72124 100644 --- a/Mathematics/3rd/Differential_equations/Images/hsector.tex +++ b/Mathematics/3rd/Differential_equations/Images/hsector.tex @@ -1,5 +1,5 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} \begin{document} \begin{tikzpicture}[decorated curves/.style={ diff --git a/Mathematics/3rd/Differential_equations/Images/linear-a.pdf b/Mathematics/3rd/Differential_equations/Images/linear-a.pdf index eb7c07a..0eebe61 100644 Binary files a/Mathematics/3rd/Differential_equations/Images/linear-a.pdf and b/Mathematics/3rd/Differential_equations/Images/linear-a.pdf differ diff --git a/Mathematics/3rd/Differential_equations/Images/linear-a.tex b/Mathematics/3rd/Differential_equations/Images/linear-a.tex index 0726c73..14e284d 100644 --- a/Mathematics/3rd/Differential_equations/Images/linear-a.tex +++ b/Mathematics/3rd/Differential_equations/Images/linear-a.tex @@ -1,5 +1,5 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} \begin{document} \begin{tikzpicture}[decorated curves/.style={ diff --git a/Mathematics/3rd/Differential_equations/Images/linear-b.pdf b/Mathematics/3rd/Differential_equations/Images/linear-b.pdf index a078943..8bd9bc6 100644 Binary files a/Mathematics/3rd/Differential_equations/Images/linear-b.pdf and b/Mathematics/3rd/Differential_equations/Images/linear-b.pdf differ diff --git a/Mathematics/3rd/Differential_equations/Images/linear-b.tex b/Mathematics/3rd/Differential_equations/Images/linear-b.tex index 7757534..ce2e5b7 100644 --- a/Mathematics/3rd/Differential_equations/Images/linear-b.tex +++ b/Mathematics/3rd/Differential_equations/Images/linear-b.tex @@ -1,5 +1,5 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} \begin{document} \begin{tikzpicture}[decorated curves/.style={ diff --git a/Mathematics/3rd/Differential_equations/Images/linear-c.pdf b/Mathematics/3rd/Differential_equations/Images/linear-c.pdf index 8ae69aa..6cbba98 100644 Binary files a/Mathematics/3rd/Differential_equations/Images/linear-c.pdf and b/Mathematics/3rd/Differential_equations/Images/linear-c.pdf differ diff --git a/Mathematics/3rd/Differential_equations/Images/linear-c.tex b/Mathematics/3rd/Differential_equations/Images/linear-c.tex index 25c09ff..8993c33 100644 --- a/Mathematics/3rd/Differential_equations/Images/linear-c.tex +++ b/Mathematics/3rd/Differential_equations/Images/linear-c.tex @@ -1,5 +1,5 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} \begin{document} \begin{tikzpicture}[decorated curves/.style={ diff --git a/Mathematics/3rd/Differential_equations/Images/linear-d.pdf b/Mathematics/3rd/Differential_equations/Images/linear-d.pdf index d80d6bd..2a26b3a 100644 Binary files a/Mathematics/3rd/Differential_equations/Images/linear-d.pdf and b/Mathematics/3rd/Differential_equations/Images/linear-d.pdf differ diff --git a/Mathematics/3rd/Differential_equations/Images/linear-d.tex b/Mathematics/3rd/Differential_equations/Images/linear-d.tex index 3ac3648..3b872c1 100644 --- a/Mathematics/3rd/Differential_equations/Images/linear-d.tex +++ b/Mathematics/3rd/Differential_equations/Images/linear-d.tex @@ -1,5 +1,5 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} \begin{document} \begin{tikzpicture}[decorated curves/.style={ diff --git a/Mathematics/3rd/Differential_equations/Images/linear-e.pdf b/Mathematics/3rd/Differential_equations/Images/linear-e.pdf index e5f21e2..a090ea3 100644 Binary files a/Mathematics/3rd/Differential_equations/Images/linear-e.pdf and b/Mathematics/3rd/Differential_equations/Images/linear-e.pdf differ diff --git a/Mathematics/3rd/Differential_equations/Images/linear-e.tex b/Mathematics/3rd/Differential_equations/Images/linear-e.tex index 6f1ca8e..2104ef4 100644 --- a/Mathematics/3rd/Differential_equations/Images/linear-e.tex +++ b/Mathematics/3rd/Differential_equations/Images/linear-e.tex @@ -1,5 +1,5 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} \begin{document} \begin{tikzpicture}[decorated curves/.style={ diff --git a/Mathematics/3rd/Differential_equations/Images/linear-f.pdf b/Mathematics/3rd/Differential_equations/Images/linear-f.pdf index bed7ee8..f515b00 100644 Binary files a/Mathematics/3rd/Differential_equations/Images/linear-f.pdf and b/Mathematics/3rd/Differential_equations/Images/linear-f.pdf differ diff --git a/Mathematics/3rd/Differential_equations/Images/linear-f.tex b/Mathematics/3rd/Differential_equations/Images/linear-f.tex index b9196e4..90f224f 100644 --- a/Mathematics/3rd/Differential_equations/Images/linear-f.tex +++ b/Mathematics/3rd/Differential_equations/Images/linear-f.tex @@ -1,5 +1,5 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} \begin{document} \begin{tikzpicture}[decorated curves/.style={ diff --git a/Mathematics/3rd/Differential_equations/Images/linear-j.pdf b/Mathematics/3rd/Differential_equations/Images/linear-j.pdf index 1070819..bf2819c 100644 Binary files a/Mathematics/3rd/Differential_equations/Images/linear-j.pdf and b/Mathematics/3rd/Differential_equations/Images/linear-j.pdf differ diff --git a/Mathematics/3rd/Differential_equations/Images/linear-j.tex b/Mathematics/3rd/Differential_equations/Images/linear-j.tex index c9f85ee..bce043e 100644 --- a/Mathematics/3rd/Differential_equations/Images/linear-j.tex +++ b/Mathematics/3rd/Differential_equations/Images/linear-j.tex @@ -1,5 +1,5 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} \begin{document} \begin{tikzpicture}[decorated curves/.style={ diff --git a/Mathematics/3rd/Differential_equations/Images/phase_portrait.pdf b/Mathematics/3rd/Differential_equations/Images/phase_portrait.pdf index 1270a6e..79e8ebb 100644 Binary files a/Mathematics/3rd/Differential_equations/Images/phase_portrait.pdf and b/Mathematics/3rd/Differential_equations/Images/phase_portrait.pdf differ diff --git a/Mathematics/3rd/Differential_equations/Images/phase_portrait.tex b/Mathematics/3rd/Differential_equations/Images/phase_portrait.tex index 1ea57e7..1ee3521 100644 --- a/Mathematics/3rd/Differential_equations/Images/phase_portrait.tex +++ b/Mathematics/3rd/Differential_equations/Images/phase_portrait.tex @@ -1,5 +1,5 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} \def\eps{0.01} \begin{document} diff --git a/Mathematics/3rd/Differential_equations/Images/phase_space.pdf b/Mathematics/3rd/Differential_equations/Images/phase_space.pdf index 76ecd23..55b40da 100644 Binary files a/Mathematics/3rd/Differential_equations/Images/phase_space.pdf and b/Mathematics/3rd/Differential_equations/Images/phase_space.pdf differ diff --git a/Mathematics/3rd/Differential_equations/Images/phase_space.tex b/Mathematics/3rd/Differential_equations/Images/phase_space.tex index 8c23bd0..e1638b9 100644 --- a/Mathematics/3rd/Differential_equations/Images/phase_space.tex +++ b/Mathematics/3rd/Differential_equations/Images/phase_space.tex @@ -1,5 +1,5 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} \begin{document} @@ -20,7 +20,6 @@ samples y=10, y dir=reverse, every axis y label/.append style={at=(ticklabel* cs:0)}] - ] % blue cone \addplot3 [draw=color_blue2,samples=200,samples y=1,domain = 0:17] ({x},{\r*cos(deg(x))},{\r*sin(deg(x))}); diff --git a/Mathematics/3rd/Differential_equations/Images/rpsector.pdf b/Mathematics/3rd/Differential_equations/Images/rpsector.pdf index ccc9183..4529a38 100644 Binary files a/Mathematics/3rd/Differential_equations/Images/rpsector.pdf and b/Mathematics/3rd/Differential_equations/Images/rpsector.pdf differ diff --git a/Mathematics/3rd/Differential_equations/Images/rpsector.tex b/Mathematics/3rd/Differential_equations/Images/rpsector.tex index 16d2a5f..23e365b 100644 --- a/Mathematics/3rd/Differential_equations/Images/rpsector.tex +++ b/Mathematics/3rd/Differential_equations/Images/rpsector.tex @@ -1,5 +1,5 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} \begin{document} \begin{tikzpicture}[,decorated separatrices/.style={ diff --git a/Mathematics/3rd/Differential_equations/Images/semistable_cycle1.pdf b/Mathematics/3rd/Differential_equations/Images/semistable_cycle1.pdf index dc50d1a..ea82425 100644 Binary files a/Mathematics/3rd/Differential_equations/Images/semistable_cycle1.pdf and b/Mathematics/3rd/Differential_equations/Images/semistable_cycle1.pdf differ diff --git a/Mathematics/3rd/Differential_equations/Images/semistable_cycle1.tex b/Mathematics/3rd/Differential_equations/Images/semistable_cycle1.tex index 0f3f94f..168f655 100644 --- a/Mathematics/3rd/Differential_equations/Images/semistable_cycle1.tex +++ b/Mathematics/3rd/Differential_equations/Images/semistable_cycle1.tex @@ -1,5 +1,5 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} \begin{document} \begin{tikzpicture}[decorated curves red/.style={ diff --git a/Mathematics/3rd/Differential_equations/Images/semistable_cycle2.pdf b/Mathematics/3rd/Differential_equations/Images/semistable_cycle2.pdf index 378a36d..f2dfb26 100644 Binary files a/Mathematics/3rd/Differential_equations/Images/semistable_cycle2.pdf and b/Mathematics/3rd/Differential_equations/Images/semistable_cycle2.pdf differ diff --git a/Mathematics/3rd/Differential_equations/Images/semistable_cycle2.tex b/Mathematics/3rd/Differential_equations/Images/semistable_cycle2.tex index 2119252..e95d5eb 100644 --- a/Mathematics/3rd/Differential_equations/Images/semistable_cycle2.tex +++ b/Mathematics/3rd/Differential_equations/Images/semistable_cycle2.tex @@ -1,5 +1,5 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} \begin{document} \begin{tikzpicture}[decorated curves red/.style={ diff --git a/Mathematics/3rd/Differential_equations/Images/singularities_dim2.pdf b/Mathematics/3rd/Differential_equations/Images/singularities_dim2.pdf index fd5e864..c6e307d 100644 Binary files a/Mathematics/3rd/Differential_equations/Images/singularities_dim2.pdf and b/Mathematics/3rd/Differential_equations/Images/singularities_dim2.pdf differ diff --git a/Mathematics/3rd/Differential_equations/Images/singularities_dim2.tex b/Mathematics/3rd/Differential_equations/Images/singularities_dim2.tex index 26deade..8b3b2f0 100644 --- a/Mathematics/3rd/Differential_equations/Images/singularities_dim2.tex +++ b/Mathematics/3rd/Differential_equations/Images/singularities_dim2.tex @@ -1,5 +1,7 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} +\usepackage{../../../../preamble_math} + \begin{document} \begin{tikzpicture}[every node/.style={scale=0.7}] diff --git a/Mathematics/3rd/Differential_equations/Images/unstable_cycle.pdf b/Mathematics/3rd/Differential_equations/Images/unstable_cycle.pdf index a1f43b1..ea0ddbc 100644 Binary files a/Mathematics/3rd/Differential_equations/Images/unstable_cycle.pdf and b/Mathematics/3rd/Differential_equations/Images/unstable_cycle.pdf differ diff --git a/Mathematics/3rd/Differential_equations/Images/unstable_cycle.tex b/Mathematics/3rd/Differential_equations/Images/unstable_cycle.tex index 318b293..c91a30a 100644 --- a/Mathematics/3rd/Differential_equations/Images/unstable_cycle.tex +++ b/Mathematics/3rd/Differential_equations/Images/unstable_cycle.tex @@ -1,5 +1,5 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} \begin{document} \begin{tikzpicture}[decorated curves red/.style={ diff --git a/Mathematics/3rd/Differential_equations/Images/vector_field.pdf b/Mathematics/3rd/Differential_equations/Images/vector_field.pdf index c157cf7..7728d29 100644 Binary files a/Mathematics/3rd/Differential_equations/Images/vector_field.pdf and b/Mathematics/3rd/Differential_equations/Images/vector_field.pdf differ diff --git a/Mathematics/3rd/Differential_equations/Images/vector_field.tex b/Mathematics/3rd/Differential_equations/Images/vector_field.tex index dd7d606..0ff8669 100644 --- a/Mathematics/3rd/Differential_equations/Images/vector_field.tex +++ b/Mathematics/3rd/Differential_equations/Images/vector_field.tex @@ -1,5 +1,5 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} \begin{document} \begin{tikzpicture} diff --git a/Mathematics/3rd/Differential_geometry/Images/involute-evolute.pdf b/Mathematics/3rd/Differential_geometry/Images/involute-evolute.pdf index beaf8dd..6db2350 100644 Binary files a/Mathematics/3rd/Differential_geometry/Images/involute-evolute.pdf and b/Mathematics/3rd/Differential_geometry/Images/involute-evolute.pdf differ diff --git a/Mathematics/3rd/Differential_geometry/Images/involute-evolute.tex b/Mathematics/3rd/Differential_geometry/Images/involute-evolute.tex index 8f716b8..afd0e38 100644 --- a/Mathematics/3rd/Differential_geometry/Images/involute-evolute.tex +++ b/Mathematics/3rd/Differential_geometry/Images/involute-evolute.tex @@ -1,5 +1,5 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} \def\n{9} \pgfplotsset{ diff --git a/Mathematics/3rd/Differential_geometry/Images/oscu-circle.pdf b/Mathematics/3rd/Differential_geometry/Images/oscu-circle.pdf index 09e270f..84deeea 100644 Binary files a/Mathematics/3rd/Differential_geometry/Images/oscu-circle.pdf and b/Mathematics/3rd/Differential_geometry/Images/oscu-circle.pdf differ diff --git a/Mathematics/3rd/Differential_geometry/Images/oscu-circle.tex b/Mathematics/3rd/Differential_geometry/Images/oscu-circle.tex index 5d2dffa..5c9b6f4 100644 --- a/Mathematics/3rd/Differential_geometry/Images/oscu-circle.tex +++ b/Mathematics/3rd/Differential_geometry/Images/oscu-circle.tex @@ -1,5 +1,6 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} +\usepackage{../../../../preamble_math} \def\r{1} \def\T{2} diff --git a/Mathematics/3rd/Differential_geometry/Images/theorem_immersions.pdf b/Mathematics/3rd/Differential_geometry/Images/theorem_immersions.pdf index 917217d..4cf3455 100644 Binary files a/Mathematics/3rd/Differential_geometry/Images/theorem_immersions.pdf and b/Mathematics/3rd/Differential_geometry/Images/theorem_immersions.pdf differ diff --git a/Mathematics/3rd/Differential_geometry/Images/theorem_immersions.tex b/Mathematics/3rd/Differential_geometry/Images/theorem_immersions.tex index 2fb7e5a..f482afd 100644 --- a/Mathematics/3rd/Differential_geometry/Images/theorem_immersions.tex +++ b/Mathematics/3rd/Differential_geometry/Images/theorem_immersions.tex @@ -1,5 +1,6 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} +\usepackage{../../../../preamble_math} \begin{document} diff --git a/Mathematics/3rd/Differential_geometry/Images/theorem_submersions.pdf b/Mathematics/3rd/Differential_geometry/Images/theorem_submersions.pdf index 7bafdf6..10e612f 100644 Binary files a/Mathematics/3rd/Differential_geometry/Images/theorem_submersions.pdf and b/Mathematics/3rd/Differential_geometry/Images/theorem_submersions.pdf differ diff --git a/Mathematics/3rd/Differential_geometry/Images/theorem_submersions.tex b/Mathematics/3rd/Differential_geometry/Images/theorem_submersions.tex index bb7400c..7100a35 100644 --- a/Mathematics/3rd/Differential_geometry/Images/theorem_submersions.tex +++ b/Mathematics/3rd/Differential_geometry/Images/theorem_submersions.tex @@ -1,5 +1,6 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} +\usepackage{../../../../preamble_math} \begin{document} diff --git a/Mathematics/3rd/Galois_theory/Images/lattice.pdf b/Mathematics/3rd/Galois_theory/Images/lattice.pdf index fc608ff..a237112 100644 Binary files a/Mathematics/3rd/Galois_theory/Images/lattice.pdf and b/Mathematics/3rd/Galois_theory/Images/lattice.pdf differ diff --git a/Mathematics/3rd/Galois_theory/Images/lattice.tex b/Mathematics/3rd/Galois_theory/Images/lattice.tex index 2119bc4..237c63e 100644 --- a/Mathematics/3rd/Galois_theory/Images/lattice.tex +++ b/Mathematics/3rd/Galois_theory/Images/lattice.tex @@ -1,5 +1,6 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} +\usepackage{../../../../preamble_math} \begin{document} \def\x{1.5} diff --git a/Mathematics/3rd/Probability/Images/normal.pdf b/Mathematics/3rd/Probability/Images/normal.pdf index 59b2530..b18f9d1 100644 Binary files a/Mathematics/3rd/Probability/Images/normal.pdf and b/Mathematics/3rd/Probability/Images/normal.pdf differ diff --git a/Mathematics/3rd/Probability/Images/normal.tex b/Mathematics/3rd/Probability/Images/normal.tex index ef382f0..4efcaff 100644 --- a/Mathematics/3rd/Probability/Images/normal.tex +++ b/Mathematics/3rd/Probability/Images/normal.tex @@ -1,5 +1,5 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} \def\m{2} % mean \def\o{0.2} % variance diff --git a/Mathematics/3rd/Statistics/Images/p-value.pdf b/Mathematics/3rd/Statistics/Images/p-value.pdf index 393ced1..ea819e9 100644 Binary files a/Mathematics/3rd/Statistics/Images/p-value.pdf and b/Mathematics/3rd/Statistics/Images/p-value.pdf differ diff --git a/Mathematics/3rd/Statistics/Images/p-value.tex b/Mathematics/3rd/Statistics/Images/p-value.tex index 59c6cd2..4f93754 100644 --- a/Mathematics/3rd/Statistics/Images/p-value.tex +++ b/Mathematics/3rd/Statistics/Images/p-value.tex @@ -1,5 +1,6 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_general} +\usepackage{../../../../preamble_tikz} \def\o{3} % variance \def\t{3} % observed value diff --git a/Mathematics/3rd/Statistics/Images/qq-plot.pdf b/Mathematics/3rd/Statistics/Images/qq-plot.pdf index ad57e7d..9fc239c 100644 Binary files a/Mathematics/3rd/Statistics/Images/qq-plot.pdf and b/Mathematics/3rd/Statistics/Images/qq-plot.pdf differ diff --git a/Mathematics/3rd/Statistics/Images/qq-plot.tex b/Mathematics/3rd/Statistics/Images/qq-plot.tex index fc41aa1..950e0da 100644 --- a/Mathematics/3rd/Statistics/Images/qq-plot.tex +++ b/Mathematics/3rd/Statistics/Images/qq-plot.tex @@ -1,5 +1,7 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} +\usepackage{../../../../preamble_math} + \begin{document} \begin{tikzpicture}[every node/.style={scale=1.5}] diff --git a/Mathematics/3rd/Statistics/Images/student-normal.pdf b/Mathematics/3rd/Statistics/Images/student-normal.pdf index 1893bd9..4996921 100644 Binary files a/Mathematics/3rd/Statistics/Images/student-normal.pdf and b/Mathematics/3rd/Statistics/Images/student-normal.pdf differ diff --git a/Mathematics/3rd/Statistics/Images/student-normal.tex b/Mathematics/3rd/Statistics/Images/student-normal.tex index aebfdeb..59706f8 100644 --- a/Mathematics/3rd/Statistics/Images/student-normal.tex +++ b/Mathematics/3rd/Statistics/Images/student-normal.tex @@ -1,5 +1,5 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} \def\n{} % level diff --git a/Mathematics/3rd/Topology/Images/circle.pdf b/Mathematics/3rd/Topology/Images/circle.pdf index e045547..e7617cc 100644 Binary files a/Mathematics/3rd/Topology/Images/circle.pdf and b/Mathematics/3rd/Topology/Images/circle.pdf differ diff --git a/Mathematics/3rd/Topology/Images/circle.tex b/Mathematics/3rd/Topology/Images/circle.tex index e911ea8..138fab3 100644 --- a/Mathematics/3rd/Topology/Images/circle.tex +++ b/Mathematics/3rd/Topology/Images/circle.tex @@ -1,5 +1,6 @@ \documentclass[border=0.05cm]{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} +\usepackage{../../../../preamble_math} \def\eps{0.06} \def\x{0.05} diff --git a/Mathematics/3rd/Topology/Images/connected_sum.pdf b/Mathematics/3rd/Topology/Images/connected_sum.pdf index b1e4443..c18e8fe 100644 Binary files a/Mathematics/3rd/Topology/Images/connected_sum.pdf and b/Mathematics/3rd/Topology/Images/connected_sum.pdf differ diff --git a/Mathematics/3rd/Topology/Images/connected_sum.tex b/Mathematics/3rd/Topology/Images/connected_sum.tex index 3a1d8ba..b3bd0a1 100644 --- a/Mathematics/3rd/Topology/Images/connected_sum.tex +++ b/Mathematics/3rd/Topology/Images/connected_sum.tex @@ -1,5 +1,7 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} +\usepackage{../../../../preamble_math} + \begin{document} \begin{tikzpicture} \def\a{2} diff --git a/Mathematics/3rd/Topology/Images/kleinbottle.pdf b/Mathematics/3rd/Topology/Images/kleinbottle.pdf index 5c9697a..d7f78fa 100644 Binary files a/Mathematics/3rd/Topology/Images/kleinbottle.pdf and b/Mathematics/3rd/Topology/Images/kleinbottle.pdf differ diff --git a/Mathematics/3rd/Topology/Images/kleinbottle.tex b/Mathematics/3rd/Topology/Images/kleinbottle.tex index ae03530..1d92b6d 100644 --- a/Mathematics/3rd/Topology/Images/kleinbottle.tex +++ b/Mathematics/3rd/Topology/Images/kleinbottle.tex @@ -1,5 +1,5 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} \begin{document} \begin{tikzpicture} diff --git a/Mathematics/3rd/Topology/Images/moebiusband.pdf b/Mathematics/3rd/Topology/Images/moebiusband.pdf index be415d5..33ba716 100644 Binary files a/Mathematics/3rd/Topology/Images/moebiusband.pdf and b/Mathematics/3rd/Topology/Images/moebiusband.pdf differ diff --git a/Mathematics/3rd/Topology/Images/moebiusband.tex b/Mathematics/3rd/Topology/Images/moebiusband.tex index 3c6851b..898e4d6 100644 --- a/Mathematics/3rd/Topology/Images/moebiusband.tex +++ b/Mathematics/3rd/Topology/Images/moebiusband.tex @@ -1,5 +1,5 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} \begin{document} \begin{tikzpicture} diff --git a/Mathematics/3rd/Topology/Images/orientable_genusG.pdf b/Mathematics/3rd/Topology/Images/orientable_genusG.pdf index bad6fe4..bdb94e3 100644 Binary files a/Mathematics/3rd/Topology/Images/orientable_genusG.pdf and b/Mathematics/3rd/Topology/Images/orientable_genusG.pdf differ diff --git a/Mathematics/3rd/Topology/Images/orientable_genusG.tex b/Mathematics/3rd/Topology/Images/orientable_genusG.tex index b6386e0..21340da 100644 --- a/Mathematics/3rd/Topology/Images/orientable_genusG.tex +++ b/Mathematics/3rd/Topology/Images/orientable_genusG.tex @@ -1,5 +1,5 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} \begin{document} \begin{tikzpicture} \def\a{2} diff --git a/Mathematics/3rd/Topology/Images/square.pdf b/Mathematics/3rd/Topology/Images/square.pdf index 050f94e..bffa1ed 100644 Binary files a/Mathematics/3rd/Topology/Images/square.pdf and b/Mathematics/3rd/Topology/Images/square.pdf differ diff --git a/Mathematics/3rd/Topology/Images/square.tex b/Mathematics/3rd/Topology/Images/square.tex index 95ef396..8579ffa 100644 --- a/Mathematics/3rd/Topology/Images/square.tex +++ b/Mathematics/3rd/Topology/Images/square.tex @@ -1,5 +1,5 @@ \documentclass[border=0.05cm]{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} \def\sepArrow{0.56} \def\sepArrowDouble{0.615} diff --git a/Mathematics/3rd/Topology/Images/torus.pdf b/Mathematics/3rd/Topology/Images/torus.pdf index d30c759..c1a5803 100644 Binary files a/Mathematics/3rd/Topology/Images/torus.pdf and b/Mathematics/3rd/Topology/Images/torus.pdf differ diff --git a/Mathematics/3rd/Topology/Images/torus.tex b/Mathematics/3rd/Topology/Images/torus.tex index cbfe415..1139f0d 100644 --- a/Mathematics/3rd/Topology/Images/torus.tex +++ b/Mathematics/3rd/Topology/Images/torus.tex @@ -1,5 +1,5 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} \def\R{3} % major radius \def\r{1.5} % minor radius diff --git a/Mathematics/3rd/Topology/Images/triangularization.pdf b/Mathematics/3rd/Topology/Images/triangularization.pdf index 170dac8..179a0ef 100644 Binary files a/Mathematics/3rd/Topology/Images/triangularization.pdf and b/Mathematics/3rd/Topology/Images/triangularization.pdf differ diff --git a/Mathematics/3rd/Topology/Images/triangularization.tex b/Mathematics/3rd/Topology/Images/triangularization.tex index 6466292..48310c3 100644 --- a/Mathematics/3rd/Topology/Images/triangularization.tex +++ b/Mathematics/3rd/Topology/Images/triangularization.tex @@ -1,5 +1,6 @@ \documentclass[border=0.05cm]{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} +\usepackage{../../../../preamble_math} \def\sepArrow{0.56} \def\sepArrowDouble{0.615} diff --git a/Mathematics/4th/Dynamical_systems/Images/blowdown.pdf b/Mathematics/4th/Dynamical_systems/Images/blowdown.pdf index 170c5de..f189965 100644 Binary files a/Mathematics/4th/Dynamical_systems/Images/blowdown.pdf and b/Mathematics/4th/Dynamical_systems/Images/blowdown.pdf differ diff --git a/Mathematics/4th/Dynamical_systems/Images/blowdown.tex b/Mathematics/4th/Dynamical_systems/Images/blowdown.tex index 8b8b204..d984902 100644 --- a/Mathematics/4th/Dynamical_systems/Images/blowdown.tex +++ b/Mathematics/4th/Dynamical_systems/Images/blowdown.tex @@ -1,5 +1,5 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} \begin{document} \begin{tikzpicture}[decorated curves/.style={ diff --git a/Mathematics/4th/Dynamical_systems/Images/blowup.pdf b/Mathematics/4th/Dynamical_systems/Images/blowup.pdf index 9056f6b..852cc2c 100644 Binary files a/Mathematics/4th/Dynamical_systems/Images/blowup.pdf and b/Mathematics/4th/Dynamical_systems/Images/blowup.pdf differ diff --git a/Mathematics/4th/Dynamical_systems/Images/blowup.tex b/Mathematics/4th/Dynamical_systems/Images/blowup.tex index d55d421..30acb73 100644 --- a/Mathematics/4th/Dynamical_systems/Images/blowup.tex +++ b/Mathematics/4th/Dynamical_systems/Images/blowup.tex @@ -1,5 +1,5 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} \begin{document} \begin{tikzpicture}[decorated curves/.style={ diff --git a/Mathematics/4th/Dynamical_systems/Images/cylinder.pdf b/Mathematics/4th/Dynamical_systems/Images/cylinder.pdf index 52917d6..52b5b40 100644 Binary files a/Mathematics/4th/Dynamical_systems/Images/cylinder.pdf and b/Mathematics/4th/Dynamical_systems/Images/cylinder.pdf differ diff --git a/Mathematics/4th/Dynamical_systems/Images/cylinder.tex b/Mathematics/4th/Dynamical_systems/Images/cylinder.tex index 2b14e93..5ff127d 100644 --- a/Mathematics/4th/Dynamical_systems/Images/cylinder.tex +++ b/Mathematics/4th/Dynamical_systems/Images/cylinder.tex @@ -1,5 +1,5 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} \pgfplotsset{ every non boxed x axis/.append style={x axis line style=-}, every non boxed y axis/.append style={y axis line style=-}} diff --git a/Mathematics/4th/Dynamical_systems/Images/fork-bif.pdf b/Mathematics/4th/Dynamical_systems/Images/fork-bif.pdf index e22ac36..a4f179b 100644 Binary files a/Mathematics/4th/Dynamical_systems/Images/fork-bif.pdf and b/Mathematics/4th/Dynamical_systems/Images/fork-bif.pdf differ diff --git a/Mathematics/4th/Dynamical_systems/Images/fork-bif.tex b/Mathematics/4th/Dynamical_systems/Images/fork-bif.tex index 587359b..b2507f4 100644 --- a/Mathematics/4th/Dynamical_systems/Images/fork-bif.tex +++ b/Mathematics/4th/Dynamical_systems/Images/fork-bif.tex @@ -1,5 +1,5 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} \begin{document} \begin{tikzpicture}[every node/.style={scale=2}] diff --git a/Mathematics/4th/Dynamical_systems/Images/hopf1.pdf b/Mathematics/4th/Dynamical_systems/Images/hopf1.pdf index a5ab433..42b903c 100644 Binary files a/Mathematics/4th/Dynamical_systems/Images/hopf1.pdf and b/Mathematics/4th/Dynamical_systems/Images/hopf1.pdf differ diff --git a/Mathematics/4th/Dynamical_systems/Images/hopf1.tex b/Mathematics/4th/Dynamical_systems/Images/hopf1.tex index a2f54b0..fc5c796 100644 --- a/Mathematics/4th/Dynamical_systems/Images/hopf1.tex +++ b/Mathematics/4th/Dynamical_systems/Images/hopf1.tex @@ -1,5 +1,5 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} \begin{document} \begin{tikzpicture}[decorated curves red/.style={ diff --git a/Mathematics/4th/Dynamical_systems/Images/hopf2.pdf b/Mathematics/4th/Dynamical_systems/Images/hopf2.pdf index b017469..02af63a 100644 Binary files a/Mathematics/4th/Dynamical_systems/Images/hopf2.pdf and b/Mathematics/4th/Dynamical_systems/Images/hopf2.pdf differ diff --git a/Mathematics/4th/Dynamical_systems/Images/hopf2.tex b/Mathematics/4th/Dynamical_systems/Images/hopf2.tex index f75cf2a..46361f0 100644 --- a/Mathematics/4th/Dynamical_systems/Images/hopf2.tex +++ b/Mathematics/4th/Dynamical_systems/Images/hopf2.tex @@ -1,5 +1,5 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} \begin{document} \begin{tikzpicture}[decorated curves red/.style={ diff --git a/Mathematics/4th/Dynamical_systems/Images/nilpot-a.pdf b/Mathematics/4th/Dynamical_systems/Images/nilpot-a.pdf index f53050e..e41510c 100644 Binary files a/Mathematics/4th/Dynamical_systems/Images/nilpot-a.pdf and b/Mathematics/4th/Dynamical_systems/Images/nilpot-a.pdf differ diff --git a/Mathematics/4th/Dynamical_systems/Images/nilpot-a.tex b/Mathematics/4th/Dynamical_systems/Images/nilpot-a.tex index 2ae27d6..be5b66b 100644 --- a/Mathematics/4th/Dynamical_systems/Images/nilpot-a.tex +++ b/Mathematics/4th/Dynamical_systems/Images/nilpot-a.tex @@ -1,5 +1,5 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} \begin{document} \begin{tikzpicture}[decorated separatrices rev/.style={ diff --git a/Mathematics/4th/Dynamical_systems/Images/nilpot-b.pdf b/Mathematics/4th/Dynamical_systems/Images/nilpot-b.pdf index d443882..1009794 100644 Binary files a/Mathematics/4th/Dynamical_systems/Images/nilpot-b.pdf and b/Mathematics/4th/Dynamical_systems/Images/nilpot-b.pdf differ diff --git a/Mathematics/4th/Dynamical_systems/Images/nilpot-b.tex b/Mathematics/4th/Dynamical_systems/Images/nilpot-b.tex index 6f63434..653ba58 100644 --- a/Mathematics/4th/Dynamical_systems/Images/nilpot-b.tex +++ b/Mathematics/4th/Dynamical_systems/Images/nilpot-b.tex @@ -1,5 +1,5 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} \begin{document} \begin{tikzpicture}[decorated separatrices rev/.style={ diff --git a/Mathematics/4th/Dynamical_systems/Images/nilpot-c.pdf b/Mathematics/4th/Dynamical_systems/Images/nilpot-c.pdf index 5187872..fda4475 100644 Binary files a/Mathematics/4th/Dynamical_systems/Images/nilpot-c.pdf and b/Mathematics/4th/Dynamical_systems/Images/nilpot-c.pdf differ diff --git a/Mathematics/4th/Dynamical_systems/Images/nilpot-c.tex b/Mathematics/4th/Dynamical_systems/Images/nilpot-c.tex index 9891386..53b2d34 100644 --- a/Mathematics/4th/Dynamical_systems/Images/nilpot-c.tex +++ b/Mathematics/4th/Dynamical_systems/Images/nilpot-c.tex @@ -1,5 +1,5 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} \begin{document} \begin{tikzpicture}[decorated separatrices rev/.style={ diff --git a/Mathematics/4th/Dynamical_systems/Images/nilpot-d.pdf b/Mathematics/4th/Dynamical_systems/Images/nilpot-d.pdf index 1c1cdc4..f9b8123 100644 Binary files a/Mathematics/4th/Dynamical_systems/Images/nilpot-d.pdf and b/Mathematics/4th/Dynamical_systems/Images/nilpot-d.pdf differ diff --git a/Mathematics/4th/Dynamical_systems/Images/nilpot-d.tex b/Mathematics/4th/Dynamical_systems/Images/nilpot-d.tex index 66c7135..06bb1f0 100644 --- a/Mathematics/4th/Dynamical_systems/Images/nilpot-d.tex +++ b/Mathematics/4th/Dynamical_systems/Images/nilpot-d.tex @@ -1,5 +1,5 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} \begin{document} \begin{tikzpicture}[decorated curves/.style={ diff --git a/Mathematics/4th/Dynamical_systems/Images/nilpot-e.pdf b/Mathematics/4th/Dynamical_systems/Images/nilpot-e.pdf index fbf1538..f3dfe0c 100644 Binary files a/Mathematics/4th/Dynamical_systems/Images/nilpot-e.pdf and b/Mathematics/4th/Dynamical_systems/Images/nilpot-e.pdf differ diff --git a/Mathematics/4th/Dynamical_systems/Images/nilpot-e.tex b/Mathematics/4th/Dynamical_systems/Images/nilpot-e.tex index acda0e8..91b6fdf 100644 --- a/Mathematics/4th/Dynamical_systems/Images/nilpot-e.tex +++ b/Mathematics/4th/Dynamical_systems/Images/nilpot-e.tex @@ -1,5 +1,5 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} \begin{document} \begin{tikzpicture}[decorated curves/.style={ diff --git a/Mathematics/4th/Dynamical_systems/Images/nilpot-f.pdf b/Mathematics/4th/Dynamical_systems/Images/nilpot-f.pdf index 9a44c52..86e2638 100644 Binary files a/Mathematics/4th/Dynamical_systems/Images/nilpot-f.pdf and b/Mathematics/4th/Dynamical_systems/Images/nilpot-f.pdf differ diff --git a/Mathematics/4th/Dynamical_systems/Images/nilpot-f.tex b/Mathematics/4th/Dynamical_systems/Images/nilpot-f.tex index 36775e2..e409b3f 100644 --- a/Mathematics/4th/Dynamical_systems/Images/nilpot-f.tex +++ b/Mathematics/4th/Dynamical_systems/Images/nilpot-f.tex @@ -1,5 +1,5 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} \begin{document} \begin{tikzpicture}[decorated curves/.style={ diff --git a/Mathematics/4th/Dynamical_systems/Images/nilpot-g.pdf b/Mathematics/4th/Dynamical_systems/Images/nilpot-g.pdf index 0699095..36f4035 100644 Binary files a/Mathematics/4th/Dynamical_systems/Images/nilpot-g.pdf and b/Mathematics/4th/Dynamical_systems/Images/nilpot-g.pdf differ diff --git a/Mathematics/4th/Dynamical_systems/Images/nilpot-g.tex b/Mathematics/4th/Dynamical_systems/Images/nilpot-g.tex index b98045d..593fd87 100644 --- a/Mathematics/4th/Dynamical_systems/Images/nilpot-g.tex +++ b/Mathematics/4th/Dynamical_systems/Images/nilpot-g.tex @@ -1,5 +1,5 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} \begin{document} \begin{tikzpicture}[decorated curves/.style={ diff --git a/Mathematics/4th/Dynamical_systems/Images/nilpot-h.pdf b/Mathematics/4th/Dynamical_systems/Images/nilpot-h.pdf index ef9c215..f225398 100644 Binary files a/Mathematics/4th/Dynamical_systems/Images/nilpot-h.pdf and b/Mathematics/4th/Dynamical_systems/Images/nilpot-h.pdf differ diff --git a/Mathematics/4th/Dynamical_systems/Images/nilpot-h.tex b/Mathematics/4th/Dynamical_systems/Images/nilpot-h.tex index 8972dc9..c57fc3d 100644 --- a/Mathematics/4th/Dynamical_systems/Images/nilpot-h.tex +++ b/Mathematics/4th/Dynamical_systems/Images/nilpot-h.tex @@ -1,5 +1,5 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} \begin{document} \begin{tikzpicture}[decorated curves/.style={ diff --git a/Mathematics/4th/Dynamical_systems/Images/nilpot-i.pdf b/Mathematics/4th/Dynamical_systems/Images/nilpot-i.pdf index c0f621d..6e4d47b 100644 Binary files a/Mathematics/4th/Dynamical_systems/Images/nilpot-i.pdf and b/Mathematics/4th/Dynamical_systems/Images/nilpot-i.pdf differ diff --git a/Mathematics/4th/Dynamical_systems/Images/nilpot-i.tex b/Mathematics/4th/Dynamical_systems/Images/nilpot-i.tex index 2ca722b..9c6a4b4 100644 --- a/Mathematics/4th/Dynamical_systems/Images/nilpot-i.tex +++ b/Mathematics/4th/Dynamical_systems/Images/nilpot-i.tex @@ -1,5 +1,5 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} \begin{document} \begin{tikzpicture}[decorated curves/.style={ diff --git a/Mathematics/4th/Dynamical_systems/Images/nilpot-j.pdf b/Mathematics/4th/Dynamical_systems/Images/nilpot-j.pdf index 1dbfb29..4aee4a6 100644 Binary files a/Mathematics/4th/Dynamical_systems/Images/nilpot-j.pdf and b/Mathematics/4th/Dynamical_systems/Images/nilpot-j.pdf differ diff --git a/Mathematics/4th/Dynamical_systems/Images/nilpot-j.tex b/Mathematics/4th/Dynamical_systems/Images/nilpot-j.tex index a9fc3bf..8347769 100644 --- a/Mathematics/4th/Dynamical_systems/Images/nilpot-j.tex +++ b/Mathematics/4th/Dynamical_systems/Images/nilpot-j.tex @@ -1,5 +1,5 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} \begin{document} \begin{tikzpicture}[decorated curves/.style={ diff --git a/Mathematics/4th/Dynamical_systems/Images/nilpot-k.pdf b/Mathematics/4th/Dynamical_systems/Images/nilpot-k.pdf index 9c07f7e..5f8f19c 100644 Binary files a/Mathematics/4th/Dynamical_systems/Images/nilpot-k.pdf and b/Mathematics/4th/Dynamical_systems/Images/nilpot-k.pdf differ diff --git a/Mathematics/4th/Dynamical_systems/Images/nilpot-k.tex b/Mathematics/4th/Dynamical_systems/Images/nilpot-k.tex index d89728b..d4cde81 100644 --- a/Mathematics/4th/Dynamical_systems/Images/nilpot-k.tex +++ b/Mathematics/4th/Dynamical_systems/Images/nilpot-k.tex @@ -1,5 +1,5 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} \begin{document} \begin{tikzpicture}[decorated curves/.style={ diff --git a/Mathematics/4th/Dynamical_systems/Images/nilpot-l.pdf b/Mathematics/4th/Dynamical_systems/Images/nilpot-l.pdf index 5e39059..f766e4e 100644 Binary files a/Mathematics/4th/Dynamical_systems/Images/nilpot-l.pdf and b/Mathematics/4th/Dynamical_systems/Images/nilpot-l.pdf differ diff --git a/Mathematics/4th/Dynamical_systems/Images/nilpot-l.tex b/Mathematics/4th/Dynamical_systems/Images/nilpot-l.tex index 89a80d0..026e098 100644 --- a/Mathematics/4th/Dynamical_systems/Images/nilpot-l.tex +++ b/Mathematics/4th/Dynamical_systems/Images/nilpot-l.tex @@ -1,5 +1,5 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} \begin{document} \begin{tikzpicture}[decorated curves/.style={ diff --git a/Mathematics/4th/Dynamical_systems/Images/nilpot-m.pdf b/Mathematics/4th/Dynamical_systems/Images/nilpot-m.pdf index 719f583..cf70672 100644 Binary files a/Mathematics/4th/Dynamical_systems/Images/nilpot-m.pdf and b/Mathematics/4th/Dynamical_systems/Images/nilpot-m.pdf differ diff --git a/Mathematics/4th/Dynamical_systems/Images/nilpot-m.tex b/Mathematics/4th/Dynamical_systems/Images/nilpot-m.tex index 23dc41c..d4a15f5 100644 --- a/Mathematics/4th/Dynamical_systems/Images/nilpot-m.tex +++ b/Mathematics/4th/Dynamical_systems/Images/nilpot-m.tex @@ -1,5 +1,5 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} \begin{document} \begin{tikzpicture}[decorated curves/.style={ diff --git a/Mathematics/4th/Dynamical_systems/Images/saddle-node_neg.pdf b/Mathematics/4th/Dynamical_systems/Images/saddle-node_neg.pdf index 6cde53a..e2caa6d 100644 Binary files a/Mathematics/4th/Dynamical_systems/Images/saddle-node_neg.pdf and b/Mathematics/4th/Dynamical_systems/Images/saddle-node_neg.pdf differ diff --git a/Mathematics/4th/Dynamical_systems/Images/saddle-node_neg.tex b/Mathematics/4th/Dynamical_systems/Images/saddle-node_neg.tex index d53a04e..3ad27b7 100644 --- a/Mathematics/4th/Dynamical_systems/Images/saddle-node_neg.tex +++ b/Mathematics/4th/Dynamical_systems/Images/saddle-node_neg.tex @@ -1,5 +1,5 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} \begin{document} \begin{tikzpicture}[decorated curves/.style={ diff --git a/Mathematics/4th/Dynamical_systems/Images/saddle-node_pos.pdf b/Mathematics/4th/Dynamical_systems/Images/saddle-node_pos.pdf index e222f40..1744778 100644 Binary files a/Mathematics/4th/Dynamical_systems/Images/saddle-node_pos.pdf and b/Mathematics/4th/Dynamical_systems/Images/saddle-node_pos.pdf differ diff --git a/Mathematics/4th/Dynamical_systems/Images/saddle-node_pos.tex b/Mathematics/4th/Dynamical_systems/Images/saddle-node_pos.tex index 7d2d32a..d420b1e 100644 --- a/Mathematics/4th/Dynamical_systems/Images/saddle-node_pos.tex +++ b/Mathematics/4th/Dynamical_systems/Images/saddle-node_pos.tex @@ -1,5 +1,5 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} \begin{document} \begin{tikzpicture}[decorated curves/.style={ diff --git a/Mathematics/4th/Dynamical_systems/Images/sn-bif.pdf b/Mathematics/4th/Dynamical_systems/Images/sn-bif.pdf index d1f3b22..9d5c55f 100644 Binary files a/Mathematics/4th/Dynamical_systems/Images/sn-bif.pdf and b/Mathematics/4th/Dynamical_systems/Images/sn-bif.pdf differ diff --git a/Mathematics/4th/Dynamical_systems/Images/sn-bif.tex b/Mathematics/4th/Dynamical_systems/Images/sn-bif.tex index 3b95702..809127e 100644 --- a/Mathematics/4th/Dynamical_systems/Images/sn-bif.tex +++ b/Mathematics/4th/Dynamical_systems/Images/sn-bif.tex @@ -1,5 +1,5 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} \begin{document} \begin{tikzpicture}[every node/.style={scale=2}] diff --git a/Mathematics/4th/Dynamical_systems/Images/trans-bif.pdf b/Mathematics/4th/Dynamical_systems/Images/trans-bif.pdf index 72e3a71..10e68f5 100644 Binary files a/Mathematics/4th/Dynamical_systems/Images/trans-bif.pdf and b/Mathematics/4th/Dynamical_systems/Images/trans-bif.pdf differ diff --git a/Mathematics/4th/Dynamical_systems/Images/trans-bif.tex b/Mathematics/4th/Dynamical_systems/Images/trans-bif.tex index 48a0862..c369f61 100644 --- a/Mathematics/4th/Dynamical_systems/Images/trans-bif.tex +++ b/Mathematics/4th/Dynamical_systems/Images/trans-bif.tex @@ -1,5 +1,5 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} \begin{document} \begin{tikzpicture}[every node/.style={scale=2}] diff --git a/Mathematics/4th/Linear_models/Images/NOTlackoffit.pdf b/Mathematics/4th/Linear_models/Images/NOTlackoffit.pdf index e16dc2d..83cb781 100644 Binary files a/Mathematics/4th/Linear_models/Images/NOTlackoffit.pdf and b/Mathematics/4th/Linear_models/Images/NOTlackoffit.pdf differ diff --git a/Mathematics/4th/Linear_models/Images/NOTlackoffit.tex b/Mathematics/4th/Linear_models/Images/NOTlackoffit.tex index 26da895..3c16e29 100644 --- a/Mathematics/4th/Linear_models/Images/NOTlackoffit.tex +++ b/Mathematics/4th/Linear_models/Images/NOTlackoffit.tex @@ -1,5 +1,5 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} \begin{document} \begin{tikzpicture}[every node/.style={scale=1.25}] diff --git a/Mathematics/4th/Linear_models/Images/confidence_band.pdf b/Mathematics/4th/Linear_models/Images/confidence_band.pdf index 9f53316..6bda382 100644 Binary files a/Mathematics/4th/Linear_models/Images/confidence_band.pdf and b/Mathematics/4th/Linear_models/Images/confidence_band.pdf differ diff --git a/Mathematics/4th/Linear_models/Images/confidence_band.tex b/Mathematics/4th/Linear_models/Images/confidence_band.tex index 7405e49..3c176c4 100644 --- a/Mathematics/4th/Linear_models/Images/confidence_band.tex +++ b/Mathematics/4th/Linear_models/Images/confidence_band.tex @@ -1,5 +1,6 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_general} +\usepackage{../../../../preamble_tikz} \begin{document} \begin{tikzpicture}[every node/.style={scale=1.25}] diff --git a/Mathematics/4th/Linear_models/Images/lackoffit.pdf b/Mathematics/4th/Linear_models/Images/lackoffit.pdf index 8b45612..f551511 100644 Binary files a/Mathematics/4th/Linear_models/Images/lackoffit.pdf and b/Mathematics/4th/Linear_models/Images/lackoffit.pdf differ diff --git a/Mathematics/4th/Linear_models/Images/lackoffit.tex b/Mathematics/4th/Linear_models/Images/lackoffit.tex index 0f66192..edbf1f9 100644 --- a/Mathematics/4th/Linear_models/Images/lackoffit.tex +++ b/Mathematics/4th/Linear_models/Images/lackoffit.tex @@ -1,5 +1,5 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} \begin{document} \begin{tikzpicture}[every node/.style={scale=1.25}] diff --git a/Mathematics/4th/Linear_models/Images/segmented_regression.pdf b/Mathematics/4th/Linear_models/Images/segmented_regression.pdf index 2076cce..efa4c35 100644 Binary files a/Mathematics/4th/Linear_models/Images/segmented_regression.pdf and b/Mathematics/4th/Linear_models/Images/segmented_regression.pdf differ diff --git a/Mathematics/4th/Linear_models/Images/segmented_regression.tex b/Mathematics/4th/Linear_models/Images/segmented_regression.tex index ff21610..8b50916 100644 --- a/Mathematics/4th/Linear_models/Images/segmented_regression.tex +++ b/Mathematics/4th/Linear_models/Images/segmented_regression.tex @@ -1,5 +1,5 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} \begin{document} \begin{tikzpicture}[every node/.style={scale=1.25}] diff --git a/Mathematics/4th/Numerical_calculus/Images/errors.pdf b/Mathematics/4th/Numerical_calculus/Images/errors.pdf index befce72..f999473 100644 Binary files a/Mathematics/4th/Numerical_calculus/Images/errors.pdf and b/Mathematics/4th/Numerical_calculus/Images/errors.pdf differ diff --git a/Mathematics/4th/Numerical_calculus/Images/errors.tex b/Mathematics/4th/Numerical_calculus/Images/errors.tex index 0326be8..f4ac6ff 100644 --- a/Mathematics/4th/Numerical_calculus/Images/errors.tex +++ b/Mathematics/4th/Numerical_calculus/Images/errors.tex @@ -1,5 +1,5 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} \begin{document} \begin{tikzpicture} diff --git a/Mathematics/4th/Numerical_calculus/Images/euler.pdf b/Mathematics/4th/Numerical_calculus/Images/euler.pdf index e4522ba..d766d9e 100644 Binary files a/Mathematics/4th/Numerical_calculus/Images/euler.pdf and b/Mathematics/4th/Numerical_calculus/Images/euler.pdf differ diff --git a/Mathematics/4th/Numerical_calculus/Images/euler.tex b/Mathematics/4th/Numerical_calculus/Images/euler.tex index 835f228..c79103b 100644 --- a/Mathematics/4th/Numerical_calculus/Images/euler.tex +++ b/Mathematics/4th/Numerical_calculus/Images/euler.tex @@ -1,5 +1,5 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} \begin{document} \begin{tikzpicture} diff --git a/Mathematics/4th/Numerical_integration_of_partial_differential_equations/Images/courant-friedrichs-lewy.pdf b/Mathematics/4th/Numerical_integration_of_partial_differential_equations/Images/courant-friedrichs-lewy.pdf index f46ecf1..437eab3 100644 Binary files a/Mathematics/4th/Numerical_integration_of_partial_differential_equations/Images/courant-friedrichs-lewy.pdf and b/Mathematics/4th/Numerical_integration_of_partial_differential_equations/Images/courant-friedrichs-lewy.pdf differ diff --git a/Mathematics/4th/Numerical_integration_of_partial_differential_equations/Images/courant-friedrichs-lewy.tex b/Mathematics/4th/Numerical_integration_of_partial_differential_equations/Images/courant-friedrichs-lewy.tex index 99491b9..529fa1e 100644 --- a/Mathematics/4th/Numerical_integration_of_partial_differential_equations/Images/courant-friedrichs-lewy.tex +++ b/Mathematics/4th/Numerical_integration_of_partial_differential_equations/Images/courant-friedrichs-lewy.tex @@ -1,5 +1,6 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} +\usepackage{../../../../preamble_math} \def\a{2} \def\lamb{0.8} diff --git a/Mathematics/4th/Numerical_integration_of_partial_differential_equations/Images/upwind.pdf b/Mathematics/4th/Numerical_integration_of_partial_differential_equations/Images/upwind.pdf index d4742e9..49d51e9 100644 Binary files a/Mathematics/4th/Numerical_integration_of_partial_differential_equations/Images/upwind.pdf and b/Mathematics/4th/Numerical_integration_of_partial_differential_equations/Images/upwind.pdf differ diff --git a/Mathematics/4th/Numerical_integration_of_partial_differential_equations/Images/upwind.tex b/Mathematics/4th/Numerical_integration_of_partial_differential_equations/Images/upwind.tex index 6cb21a4..ec42b53 100644 --- a/Mathematics/4th/Numerical_integration_of_partial_differential_equations/Images/upwind.tex +++ b/Mathematics/4th/Numerical_integration_of_partial_differential_equations/Images/upwind.tex @@ -1,5 +1,5 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} \def\a{1} \def\lamb{0.8} diff --git a/Mathematics/4th/Partial_differential_equations/Images/traffic_char.pdf b/Mathematics/4th/Partial_differential_equations/Images/traffic_char.pdf index a5b5cdc..f357387 100644 Binary files a/Mathematics/4th/Partial_differential_equations/Images/traffic_char.pdf and b/Mathematics/4th/Partial_differential_equations/Images/traffic_char.pdf differ diff --git a/Mathematics/4th/Partial_differential_equations/Images/traffic_char.tex b/Mathematics/4th/Partial_differential_equations/Images/traffic_char.tex index f022359..e5e191b 100644 --- a/Mathematics/4th/Partial_differential_equations/Images/traffic_char.tex +++ b/Mathematics/4th/Partial_differential_equations/Images/traffic_char.tex @@ -1,5 +1,6 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} +\usepackage{../../../../preamble_math} \begin{document} \begin{tikzpicture} diff --git a/Mathematics/4th/Partial_differential_equations/Images/waves_char.pdf b/Mathematics/4th/Partial_differential_equations/Images/waves_char.pdf index 77a2287..f499de3 100644 Binary files a/Mathematics/4th/Partial_differential_equations/Images/waves_char.pdf and b/Mathematics/4th/Partial_differential_equations/Images/waves_char.pdf differ diff --git a/Mathematics/4th/Partial_differential_equations/Images/waves_char.tex b/Mathematics/4th/Partial_differential_equations/Images/waves_char.tex index e9eef2c..ffcfcb6 100644 --- a/Mathematics/4th/Partial_differential_equations/Images/waves_char.tex +++ b/Mathematics/4th/Partial_differential_equations/Images/waves_char.tex @@ -1,5 +1,5 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} \begin{document} \begin{tikzpicture} diff --git a/Mathematics/4th/Partial_differential_equations/Images/waves_char_solve.pdf b/Mathematics/4th/Partial_differential_equations/Images/waves_char_solve.pdf index 6ed5199..1cf7955 100644 Binary files a/Mathematics/4th/Partial_differential_equations/Images/waves_char_solve.pdf and b/Mathematics/4th/Partial_differential_equations/Images/waves_char_solve.pdf differ diff --git a/Mathematics/4th/Partial_differential_equations/Images/waves_char_solve.tex b/Mathematics/4th/Partial_differential_equations/Images/waves_char_solve.tex index 25df058..f170af2 100644 --- a/Mathematics/4th/Partial_differential_equations/Images/waves_char_solve.tex +++ b/Mathematics/4th/Partial_differential_equations/Images/waves_char_solve.tex @@ -1,5 +1,6 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_general} +\usepackage{../../../../preamble_tikz} \begin{document} \begin{tikzpicture} diff --git a/Mathematics/4th/Real_and_functional_analysis/Images/young.pdf b/Mathematics/4th/Real_and_functional_analysis/Images/young.pdf index d2515b2..16e1a9d 100644 Binary files a/Mathematics/4th/Real_and_functional_analysis/Images/young.pdf and b/Mathematics/4th/Real_and_functional_analysis/Images/young.pdf differ diff --git a/Mathematics/4th/Real_and_functional_analysis/Images/young.tex b/Mathematics/4th/Real_and_functional_analysis/Images/young.tex index d4f1516..cdb0fc3 100644 --- a/Mathematics/4th/Real_and_functional_analysis/Images/young.tex +++ b/Mathematics/4th/Real_and_functional_analysis/Images/young.tex @@ -1,5 +1,5 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} \begin{document} \begin{tikzpicture} diff --git a/Mathematics/4th/Stochastic_processes/Images/brownianMotion.pdf b/Mathematics/4th/Stochastic_processes/Images/brownianMotion.pdf index 085e19b..9985d44 100644 Binary files a/Mathematics/4th/Stochastic_processes/Images/brownianMotion.pdf and b/Mathematics/4th/Stochastic_processes/Images/brownianMotion.pdf differ diff --git a/Mathematics/4th/Stochastic_processes/Images/brownianMotion.tex b/Mathematics/4th/Stochastic_processes/Images/brownianMotion.tex index d4f85d4..9589592 100644 --- a/Mathematics/4th/Stochastic_processes/Images/brownianMotion.tex +++ b/Mathematics/4th/Stochastic_processes/Images/brownianMotion.tex @@ -1,5 +1,5 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} \begin{document} \begin{tikzpicture} diff --git a/Mathematics/4th/Stochastic_processes/Images/randomWalk.pdf b/Mathematics/4th/Stochastic_processes/Images/randomWalk.pdf index cdf95f9..8ba26b0 100644 Binary files a/Mathematics/4th/Stochastic_processes/Images/randomWalk.pdf and b/Mathematics/4th/Stochastic_processes/Images/randomWalk.pdf differ diff --git a/Mathematics/4th/Stochastic_processes/Images/randomWalk.tex b/Mathematics/4th/Stochastic_processes/Images/randomWalk.tex index 5b081d2..89cd44b 100644 --- a/Mathematics/4th/Stochastic_processes/Images/randomWalk.tex +++ b/Mathematics/4th/Stochastic_processes/Images/randomWalk.tex @@ -1,5 +1,5 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} \begin{document} \begin{tikzpicture} diff --git a/Physics/Basic/Classical_mechanics/Images/LC.pdf b/Physics/Basic/Classical_mechanics/Images/LC.pdf index d041ca9..ee3aa81 100644 Binary files a/Physics/Basic/Classical_mechanics/Images/LC.pdf and b/Physics/Basic/Classical_mechanics/Images/LC.pdf differ diff --git a/Physics/Basic/Classical_mechanics/Images/LC.tex b/Physics/Basic/Classical_mechanics/Images/LC.tex index b0601d0..125b3bd 100644 --- a/Physics/Basic/Classical_mechanics/Images/LC.tex +++ b/Physics/Basic/Classical_mechanics/Images/LC.tex @@ -1,5 +1,5 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} \begin{document} \begin{circuitikz} diff --git a/Physics/Basic/Classical_mechanics/Images/RLC-genP.pdf b/Physics/Basic/Classical_mechanics/Images/RLC-genP.pdf index 586c440..943333c 100644 Binary files a/Physics/Basic/Classical_mechanics/Images/RLC-genP.pdf and b/Physics/Basic/Classical_mechanics/Images/RLC-genP.pdf differ diff --git a/Physics/Basic/Classical_mechanics/Images/RLC-genP.tex b/Physics/Basic/Classical_mechanics/Images/RLC-genP.tex index a4fdd9e..1367afc 100644 --- a/Physics/Basic/Classical_mechanics/Images/RLC-genP.tex +++ b/Physics/Basic/Classical_mechanics/Images/RLC-genP.tex @@ -1,5 +1,6 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} +\usepackage{../../../../preamble_math} \begin{document} \begin{circuitikz} diff --git a/Physics/Basic/Classical_mechanics/Images/RLC-genS.pdf b/Physics/Basic/Classical_mechanics/Images/RLC-genS.pdf index 2f737fa..8b7c4ac 100644 Binary files a/Physics/Basic/Classical_mechanics/Images/RLC-genS.pdf and b/Physics/Basic/Classical_mechanics/Images/RLC-genS.pdf differ diff --git a/Physics/Basic/Classical_mechanics/Images/RLC-genS.tex b/Physics/Basic/Classical_mechanics/Images/RLC-genS.tex index a9b1d77..8557153 100644 --- a/Physics/Basic/Classical_mechanics/Images/RLC-genS.tex +++ b/Physics/Basic/Classical_mechanics/Images/RLC-genS.tex @@ -1,5 +1,6 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} +\usepackage{../../../../preamble_math} \begin{document} \begin{circuitikz} diff --git a/Physics/Basic/Classical_mechanics/Images/RLC.pdf b/Physics/Basic/Classical_mechanics/Images/RLC.pdf index fa03afa..f8a2605 100644 Binary files a/Physics/Basic/Classical_mechanics/Images/RLC.pdf and b/Physics/Basic/Classical_mechanics/Images/RLC.pdf differ diff --git a/Physics/Basic/Classical_mechanics/Images/RLC.tex b/Physics/Basic/Classical_mechanics/Images/RLC.tex index 6506deb..0e5feb2 100644 --- a/Physics/Basic/Classical_mechanics/Images/RLC.tex +++ b/Physics/Basic/Classical_mechanics/Images/RLC.tex @@ -1,5 +1,5 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} \begin{document} \begin{circuitikz} diff --git a/Physics/Basic/Classical_mechanics/Images/areal_vel.pdf b/Physics/Basic/Classical_mechanics/Images/areal_vel.pdf index 0d3b4cd..cafa7c3 100644 Binary files a/Physics/Basic/Classical_mechanics/Images/areal_vel.pdf and b/Physics/Basic/Classical_mechanics/Images/areal_vel.pdf differ diff --git a/Physics/Basic/Classical_mechanics/Images/areal_vel.tex b/Physics/Basic/Classical_mechanics/Images/areal_vel.tex index 96fd1a3..f3ed224 100644 --- a/Physics/Basic/Classical_mechanics/Images/areal_vel.tex +++ b/Physics/Basic/Classical_mechanics/Images/areal_vel.tex @@ -1,5 +1,5 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} \def\a{2} \def\b{1.5} \begin{document} diff --git a/Physics/Basic/Classical_mechanics/Images/conics.pdf b/Physics/Basic/Classical_mechanics/Images/conics.pdf index 2666bdc..fea32ef 100644 Binary files a/Physics/Basic/Classical_mechanics/Images/conics.pdf and b/Physics/Basic/Classical_mechanics/Images/conics.pdf differ diff --git a/Physics/Basic/Classical_mechanics/Images/conics.tex b/Physics/Basic/Classical_mechanics/Images/conics.tex index ce1c0f1..706f7db 100644 --- a/Physics/Basic/Classical_mechanics/Images/conics.tex +++ b/Physics/Basic/Classical_mechanics/Images/conics.tex @@ -1,5 +1,5 @@ \documentclass[tikz]{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} \begin{document} \begin{tikzpicture} diff --git a/Physics/Basic/Classical_mechanics/Images/ellipse.pdf b/Physics/Basic/Classical_mechanics/Images/ellipse.pdf index 4c4ee1d..8f08386 100644 Binary files a/Physics/Basic/Classical_mechanics/Images/ellipse.pdf and b/Physics/Basic/Classical_mechanics/Images/ellipse.pdf differ diff --git a/Physics/Basic/Classical_mechanics/Images/ellipse.tex b/Physics/Basic/Classical_mechanics/Images/ellipse.tex index 78f10df..8b67f85 100644 --- a/Physics/Basic/Classical_mechanics/Images/ellipse.tex +++ b/Physics/Basic/Classical_mechanics/Images/ellipse.tex @@ -1,5 +1,5 @@ \documentclass[tikz]{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} \begin{document} \begin{tikzpicture} diff --git a/Physics/Basic/Classical_mechanics/Images/hyperbola.pdf b/Physics/Basic/Classical_mechanics/Images/hyperbola.pdf index 5131748..076d9ea 100644 Binary files a/Physics/Basic/Classical_mechanics/Images/hyperbola.pdf and b/Physics/Basic/Classical_mechanics/Images/hyperbola.pdf differ diff --git a/Physics/Basic/Classical_mechanics/Images/hyperbola.tex b/Physics/Basic/Classical_mechanics/Images/hyperbola.tex index e667f04..77d43b4 100644 --- a/Physics/Basic/Classical_mechanics/Images/hyperbola.tex +++ b/Physics/Basic/Classical_mechanics/Images/hyperbola.tex @@ -1,5 +1,5 @@ \documentclass[tikz]{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} \begin{document} \begin{tikzpicture}[every node/.style={scale=0.9}] diff --git a/Physics/Basic/Classical_mechanics/Images/physical_pendulum.pdf b/Physics/Basic/Classical_mechanics/Images/physical_pendulum.pdf index 6b9a014..12837f5 100644 Binary files a/Physics/Basic/Classical_mechanics/Images/physical_pendulum.pdf and b/Physics/Basic/Classical_mechanics/Images/physical_pendulum.pdf differ diff --git a/Physics/Basic/Classical_mechanics/Images/physical_pendulum.tex b/Physics/Basic/Classical_mechanics/Images/physical_pendulum.tex index 2816a33..d1141b1 100644 --- a/Physics/Basic/Classical_mechanics/Images/physical_pendulum.tex +++ b/Physics/Basic/Classical_mechanics/Images/physical_pendulum.tex @@ -1,5 +1,5 @@ \documentclass[tikz]{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} \begin{document} \begin{tikzpicture} diff --git a/Physics/Basic/Classical_mechanics/Images/ress_amplitude.pdf b/Physics/Basic/Classical_mechanics/Images/ress_amplitude.pdf index 6c8fa69..7e9493b 100644 Binary files a/Physics/Basic/Classical_mechanics/Images/ress_amplitude.pdf and b/Physics/Basic/Classical_mechanics/Images/ress_amplitude.pdf differ diff --git a/Physics/Basic/Classical_mechanics/Images/ress_amplitude.tex b/Physics/Basic/Classical_mechanics/Images/ress_amplitude.tex index 724b847..0ce285b 100644 --- a/Physics/Basic/Classical_mechanics/Images/ress_amplitude.tex +++ b/Physics/Basic/Classical_mechanics/Images/ress_amplitude.tex @@ -1,5 +1,5 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} \begin{document} \begin{tikzpicture} diff --git a/Physics/Basic/Classical_mechanics/Images/ress_energy.pdf b/Physics/Basic/Classical_mechanics/Images/ress_energy.pdf index cb4abf1..53823b9 100644 Binary files a/Physics/Basic/Classical_mechanics/Images/ress_energy.pdf and b/Physics/Basic/Classical_mechanics/Images/ress_energy.pdf differ diff --git a/Physics/Basic/Classical_mechanics/Images/ress_energy.tex b/Physics/Basic/Classical_mechanics/Images/ress_energy.tex index a5c1add..e3677f1 100644 --- a/Physics/Basic/Classical_mechanics/Images/ress_energy.tex +++ b/Physics/Basic/Classical_mechanics/Images/ress_energy.tex @@ -1,5 +1,6 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} +\usepackage{../../../../preamble_math} \begin{document} \begin{tikzpicture} diff --git a/Physics/Basic/Classical_mechanics/Images/simple_pendulum.pdf b/Physics/Basic/Classical_mechanics/Images/simple_pendulum.pdf index f9ec323..eb95bff 100644 Binary files a/Physics/Basic/Classical_mechanics/Images/simple_pendulum.pdf and b/Physics/Basic/Classical_mechanics/Images/simple_pendulum.pdf differ diff --git a/Physics/Basic/Classical_mechanics/Images/simple_pendulum.tex b/Physics/Basic/Classical_mechanics/Images/simple_pendulum.tex index 2430fc5..da38701 100644 --- a/Physics/Basic/Classical_mechanics/Images/simple_pendulum.tex +++ b/Physics/Basic/Classical_mechanics/Images/simple_pendulum.tex @@ -1,5 +1,5 @@ \documentclass[tikz]{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} \begin{document} \begin{tikzpicture} diff --git a/Physics/Basic/Classical_mechanics/Images/spring.pdf b/Physics/Basic/Classical_mechanics/Images/spring.pdf index d6eba44..dacad85 100644 Binary files a/Physics/Basic/Classical_mechanics/Images/spring.pdf and b/Physics/Basic/Classical_mechanics/Images/spring.pdf differ diff --git a/Physics/Basic/Classical_mechanics/Images/spring.tex b/Physics/Basic/Classical_mechanics/Images/spring.tex index 0af5321..0e9c555 100644 --- a/Physics/Basic/Classical_mechanics/Images/spring.tex +++ b/Physics/Basic/Classical_mechanics/Images/spring.tex @@ -1,5 +1,5 @@ \documentclass[tikz]{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} \begin{document} \begin{tikzpicture} diff --git a/Physics/Basic/Classical_mechanics/Images/springs.pdf b/Physics/Basic/Classical_mechanics/Images/springs.pdf index 8d2e13c..6f5eded 100644 Binary files a/Physics/Basic/Classical_mechanics/Images/springs.pdf and b/Physics/Basic/Classical_mechanics/Images/springs.pdf differ diff --git a/Physics/Basic/Classical_mechanics/Images/springs.tex b/Physics/Basic/Classical_mechanics/Images/springs.tex index 65ffe2a..bbb72d7 100644 --- a/Physics/Basic/Classical_mechanics/Images/springs.tex +++ b/Physics/Basic/Classical_mechanics/Images/springs.tex @@ -1,5 +1,5 @@ \documentclass[tikz]{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} \begin{document} \begin{tikzpicture} diff --git a/Physics/Basic/Electricity_and_magnetism/Images/dipole.pdf b/Physics/Basic/Electricity_and_magnetism/Images/dipole.pdf index 0de854c..af25c97 100644 Binary files a/Physics/Basic/Electricity_and_magnetism/Images/dipole.pdf and b/Physics/Basic/Electricity_and_magnetism/Images/dipole.pdf differ diff --git a/Physics/Basic/Electricity_and_magnetism/Images/dipole.tex b/Physics/Basic/Electricity_and_magnetism/Images/dipole.tex index e23148f..9c71e36 100644 --- a/Physics/Basic/Electricity_and_magnetism/Images/dipole.tex +++ b/Physics/Basic/Electricity_and_magnetism/Images/dipole.tex @@ -1,5 +1,6 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} +\usepackage{../../../../preamble_math} \begin{document} \begin{tikzpicture}[decoration={markings, diff --git a/Physics/Basic/Electricity_and_magnetism/Images/finite_wire.pdf b/Physics/Basic/Electricity_and_magnetism/Images/finite_wire.pdf index 3995c64..67ad9c3 100644 Binary files a/Physics/Basic/Electricity_and_magnetism/Images/finite_wire.pdf and b/Physics/Basic/Electricity_and_magnetism/Images/finite_wire.pdf differ diff --git a/Physics/Basic/Electricity_and_magnetism/Images/finite_wire.tex b/Physics/Basic/Electricity_and_magnetism/Images/finite_wire.tex index 74010bd..937e625 100644 --- a/Physics/Basic/Electricity_and_magnetism/Images/finite_wire.tex +++ b/Physics/Basic/Electricity_and_magnetism/Images/finite_wire.tex @@ -1,5 +1,6 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} +\usepackage{../../../../preamble_math} \begin{document} \begin{tikzpicture} diff --git a/Physics/Basic/Electricity_and_magnetism/Images/hall_effect.pdf b/Physics/Basic/Electricity_and_magnetism/Images/hall_effect.pdf index a3f9bbe..65b5482 100644 Binary files a/Physics/Basic/Electricity_and_magnetism/Images/hall_effect.pdf and b/Physics/Basic/Electricity_and_magnetism/Images/hall_effect.pdf differ diff --git a/Physics/Basic/Electricity_and_magnetism/Images/hall_effect.tex b/Physics/Basic/Electricity_and_magnetism/Images/hall_effect.tex index 476f34a..ca1397a 100644 --- a/Physics/Basic/Electricity_and_magnetism/Images/hall_effect.tex +++ b/Physics/Basic/Electricity_and_magnetism/Images/hall_effect.tex @@ -1,5 +1,6 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} +\usepackage{../../../../preamble_math} \begin{document} \begin{circuitikz} diff --git a/Physics/Basic/Electricity_and_magnetism/Images/solenoid.pdf b/Physics/Basic/Electricity_and_magnetism/Images/solenoid.pdf index 73cbbeb..37415cd 100644 Binary files a/Physics/Basic/Electricity_and_magnetism/Images/solenoid.pdf and b/Physics/Basic/Electricity_and_magnetism/Images/solenoid.pdf differ diff --git a/Physics/Basic/Electricity_and_magnetism/Images/solenoid.tex b/Physics/Basic/Electricity_and_magnetism/Images/solenoid.tex index 4bafd2a..c1cf2e6 100644 --- a/Physics/Basic/Electricity_and_magnetism/Images/solenoid.tex +++ b/Physics/Basic/Electricity_and_magnetism/Images/solenoid.tex @@ -1,5 +1,6 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} +\usepackage{../../../../preamble_math} \begin{document} \begin{tikzpicture} diff --git a/Physics/Basic/Electromagnetism/Images/method_images.pdf b/Physics/Basic/Electromagnetism/Images/method_images.pdf index 638be10..3bbd9cf 100644 Binary files a/Physics/Basic/Electromagnetism/Images/method_images.pdf and b/Physics/Basic/Electromagnetism/Images/method_images.pdf differ diff --git a/Physics/Basic/Electromagnetism/Images/method_images.tex b/Physics/Basic/Electromagnetism/Images/method_images.tex index fe08a7a..a5c85bd 100644 --- a/Physics/Basic/Electromagnetism/Images/method_images.tex +++ b/Physics/Basic/Electromagnetism/Images/method_images.tex @@ -1,5 +1,5 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} \begin{document} \begin{tikzpicture} diff --git a/Physics/Basic/Mechanics_and_special_relativity/Images/compton.pdf b/Physics/Basic/Mechanics_and_special_relativity/Images/compton.pdf index b20faa2..415ba90 100644 Binary files a/Physics/Basic/Mechanics_and_special_relativity/Images/compton.pdf and b/Physics/Basic/Mechanics_and_special_relativity/Images/compton.pdf differ diff --git a/Physics/Basic/Mechanics_and_special_relativity/Images/compton.tex b/Physics/Basic/Mechanics_and_special_relativity/Images/compton.tex index aecdc6d..dc82991 100644 --- a/Physics/Basic/Mechanics_and_special_relativity/Images/compton.tex +++ b/Physics/Basic/Mechanics_and_special_relativity/Images/compton.tex @@ -1,5 +1,5 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} \begin{document} \begin{tikzpicture} diff --git a/Physics/Basic/Mechanics_and_special_relativity/Images/doppler.pdf b/Physics/Basic/Mechanics_and_special_relativity/Images/doppler.pdf index 9119dd3..dd5be9a 100644 Binary files a/Physics/Basic/Mechanics_and_special_relativity/Images/doppler.pdf and b/Physics/Basic/Mechanics_and_special_relativity/Images/doppler.pdf differ diff --git a/Physics/Basic/Mechanics_and_special_relativity/Images/doppler.tex b/Physics/Basic/Mechanics_and_special_relativity/Images/doppler.tex index e2c1b94..2a63d7a 100644 --- a/Physics/Basic/Mechanics_and_special_relativity/Images/doppler.tex +++ b/Physics/Basic/Mechanics_and_special_relativity/Images/doppler.tex @@ -1,5 +1,5 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} \begin{document} \begin{tikzpicture} diff --git a/Physics/Basic/Mechanics_and_special_relativity/Images/elastic_force.pdf b/Physics/Basic/Mechanics_and_special_relativity/Images/elastic_force.pdf index cc7c088..0be3bcb 100644 Binary files a/Physics/Basic/Mechanics_and_special_relativity/Images/elastic_force.pdf and b/Physics/Basic/Mechanics_and_special_relativity/Images/elastic_force.pdf differ diff --git a/Physics/Basic/Mechanics_and_special_relativity/Images/elastic_force.tex b/Physics/Basic/Mechanics_and_special_relativity/Images/elastic_force.tex index f47b2f9..c92b12c 100644 --- a/Physics/Basic/Mechanics_and_special_relativity/Images/elastic_force.tex +++ b/Physics/Basic/Mechanics_and_special_relativity/Images/elastic_force.tex @@ -1,5 +1,6 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} +\usepackage{../../../../preamble_math} \begin{document} \begin{tikzpicture} diff --git a/Physics/Basic/Mechanics_and_special_relativity/Images/inertial_force.pdf b/Physics/Basic/Mechanics_and_special_relativity/Images/inertial_force.pdf index 05cbdc9..3f7aeef 100644 Binary files a/Physics/Basic/Mechanics_and_special_relativity/Images/inertial_force.pdf and b/Physics/Basic/Mechanics_and_special_relativity/Images/inertial_force.pdf differ diff --git a/Physics/Basic/Mechanics_and_special_relativity/Images/inertial_force.tex b/Physics/Basic/Mechanics_and_special_relativity/Images/inertial_force.tex index 87a8568..8cefa89 100644 --- a/Physics/Basic/Mechanics_and_special_relativity/Images/inertial_force.tex +++ b/Physics/Basic/Mechanics_and_special_relativity/Images/inertial_force.tex @@ -1,5 +1,6 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} +\usepackage{../../../../preamble_math} \begin{document} diff --git a/Physics/Basic/Mechanics_and_special_relativity/Images/laminar_turbulent.pdf b/Physics/Basic/Mechanics_and_special_relativity/Images/laminar_turbulent.pdf index f9344af..4b1175a 100644 Binary files a/Physics/Basic/Mechanics_and_special_relativity/Images/laminar_turbulent.pdf and b/Physics/Basic/Mechanics_and_special_relativity/Images/laminar_turbulent.pdf differ diff --git a/Physics/Basic/Mechanics_and_special_relativity/Images/laminar_turbulent.tex b/Physics/Basic/Mechanics_and_special_relativity/Images/laminar_turbulent.tex index 804b6a0..268340c 100644 --- a/Physics/Basic/Mechanics_and_special_relativity/Images/laminar_turbulent.tex +++ b/Physics/Basic/Mechanics_and_special_relativity/Images/laminar_turbulent.tex @@ -1,5 +1,5 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} \begin{document} diff --git a/Physics/Basic/Mechanics_and_special_relativity/Images/minkowski.pdf b/Physics/Basic/Mechanics_and_special_relativity/Images/minkowski.pdf index 6a16049..bf02034 100644 Binary files a/Physics/Basic/Mechanics_and_special_relativity/Images/minkowski.pdf and b/Physics/Basic/Mechanics_and_special_relativity/Images/minkowski.pdf differ diff --git a/Physics/Basic/Mechanics_and_special_relativity/Images/minkowski.tex b/Physics/Basic/Mechanics_and_special_relativity/Images/minkowski.tex index 5104dac..e62ec8a 100644 --- a/Physics/Basic/Mechanics_and_special_relativity/Images/minkowski.tex +++ b/Physics/Basic/Mechanics_and_special_relativity/Images/minkowski.tex @@ -1,5 +1,5 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} \begin{document} \begin{tikzpicture}[scale=2] diff --git a/Physics/Basic/Mechanics_and_special_relativity/Images/projectile.pdf b/Physics/Basic/Mechanics_and_special_relativity/Images/projectile.pdf index f59ce2c..0f17957 100644 Binary files a/Physics/Basic/Mechanics_and_special_relativity/Images/projectile.pdf and b/Physics/Basic/Mechanics_and_special_relativity/Images/projectile.pdf differ diff --git a/Physics/Basic/Mechanics_and_special_relativity/Images/projectile.tex b/Physics/Basic/Mechanics_and_special_relativity/Images/projectile.tex index bf5ee5e..fb3cd9d 100644 --- a/Physics/Basic/Mechanics_and_special_relativity/Images/projectile.tex +++ b/Physics/Basic/Mechanics_and_special_relativity/Images/projectile.tex @@ -1,5 +1,6 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} +\usepackage{../../../../preamble_math} \begin{document} diff --git a/Physics/Basic/Mechanics_and_special_relativity/Images/viscous_force.pdf b/Physics/Basic/Mechanics_and_special_relativity/Images/viscous_force.pdf index b741a79..a34c412 100644 Binary files a/Physics/Basic/Mechanics_and_special_relativity/Images/viscous_force.pdf and b/Physics/Basic/Mechanics_and_special_relativity/Images/viscous_force.pdf differ diff --git a/Physics/Basic/Mechanics_and_special_relativity/Images/viscous_force.tex b/Physics/Basic/Mechanics_and_special_relativity/Images/viscous_force.tex index 309e70c..ebd1889 100644 --- a/Physics/Basic/Mechanics_and_special_relativity/Images/viscous_force.tex +++ b/Physics/Basic/Mechanics_and_special_relativity/Images/viscous_force.tex @@ -1,5 +1,6 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} +\usepackage{../../../../preamble_math} \begin{document} \pgfdeclarelayer{pre main} % to avoid a warning diff --git a/Physics/Basic/Structure_of_matter_and_thermodynamics/Images/band_theory.pdf b/Physics/Basic/Structure_of_matter_and_thermodynamics/Images/band_theory.pdf index fde0ea0..46ff861 100644 Binary files a/Physics/Basic/Structure_of_matter_and_thermodynamics/Images/band_theory.pdf and b/Physics/Basic/Structure_of_matter_and_thermodynamics/Images/band_theory.pdf differ diff --git a/Physics/Basic/Structure_of_matter_and_thermodynamics/Images/band_theory.tex b/Physics/Basic/Structure_of_matter_and_thermodynamics/Images/band_theory.tex index ff2e1e4..c27a115 100644 --- a/Physics/Basic/Structure_of_matter_and_thermodynamics/Images/band_theory.tex +++ b/Physics/Basic/Structure_of_matter_and_thermodynamics/Images/band_theory.tex @@ -1,5 +1,5 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} \begin{document} \begin{tikzpicture} diff --git a/Physics/Basic/Structure_of_matter_and_thermodynamics/Images/carnot.pdf b/Physics/Basic/Structure_of_matter_and_thermodynamics/Images/carnot.pdf index 876bf82..4a2c0fe 100644 Binary files a/Physics/Basic/Structure_of_matter_and_thermodynamics/Images/carnot.pdf and b/Physics/Basic/Structure_of_matter_and_thermodynamics/Images/carnot.pdf differ diff --git a/Physics/Basic/Structure_of_matter_and_thermodynamics/Images/carnot.tex b/Physics/Basic/Structure_of_matter_and_thermodynamics/Images/carnot.tex index 4aa452b..39e803a 100644 --- a/Physics/Basic/Structure_of_matter_and_thermodynamics/Images/carnot.tex +++ b/Physics/Basic/Structure_of_matter_and_thermodynamics/Images/carnot.tex @@ -1,5 +1,6 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} +\usepackage{../../../../preamble_math} \begin{document} \begin{tikzpicture}[scale=1, every node/.style={scale=0.5}] diff --git a/Physics/Basic/Structure_of_matter_and_thermodynamics/Images/decay_chain.pdf b/Physics/Basic/Structure_of_matter_and_thermodynamics/Images/decay_chain.pdf index 5bae981..22eb06d 100644 Binary files a/Physics/Basic/Structure_of_matter_and_thermodynamics/Images/decay_chain.pdf and b/Physics/Basic/Structure_of_matter_and_thermodynamics/Images/decay_chain.pdf differ diff --git a/Physics/Basic/Structure_of_matter_and_thermodynamics/Images/decay_chain.tex b/Physics/Basic/Structure_of_matter_and_thermodynamics/Images/decay_chain.tex index ea64710..dbd033b 100644 --- a/Physics/Basic/Structure_of_matter_and_thermodynamics/Images/decay_chain.tex +++ b/Physics/Basic/Structure_of_matter_and_thermodynamics/Images/decay_chain.tex @@ -1,5 +1,5 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} \begin{document} \begin{tikzpicture} diff --git a/Physics/Basic/Structure_of_matter_and_thermodynamics/Images/equilibrium_meta.pdf b/Physics/Basic/Structure_of_matter_and_thermodynamics/Images/equilibrium_meta.pdf index c35727c..a6e7639 100644 Binary files a/Physics/Basic/Structure_of_matter_and_thermodynamics/Images/equilibrium_meta.pdf and b/Physics/Basic/Structure_of_matter_and_thermodynamics/Images/equilibrium_meta.pdf differ diff --git a/Physics/Basic/Structure_of_matter_and_thermodynamics/Images/equilibrium_meta.tex b/Physics/Basic/Structure_of_matter_and_thermodynamics/Images/equilibrium_meta.tex index 4433abd..4e0696b 100644 --- a/Physics/Basic/Structure_of_matter_and_thermodynamics/Images/equilibrium_meta.tex +++ b/Physics/Basic/Structure_of_matter_and_thermodynamics/Images/equilibrium_meta.tex @@ -1,5 +1,5 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} \begin{document} \begin{tikzpicture} diff --git a/Physics/Basic/Structure_of_matter_and_thermodynamics/Images/equilibrium_neutr.pdf b/Physics/Basic/Structure_of_matter_and_thermodynamics/Images/equilibrium_neutr.pdf index dd9a8f7..3571fc5 100644 Binary files a/Physics/Basic/Structure_of_matter_and_thermodynamics/Images/equilibrium_neutr.pdf and b/Physics/Basic/Structure_of_matter_and_thermodynamics/Images/equilibrium_neutr.pdf differ diff --git a/Physics/Basic/Structure_of_matter_and_thermodynamics/Images/equilibrium_neutr.tex b/Physics/Basic/Structure_of_matter_and_thermodynamics/Images/equilibrium_neutr.tex index d7670af..5126f0d 100644 --- a/Physics/Basic/Structure_of_matter_and_thermodynamics/Images/equilibrium_neutr.tex +++ b/Physics/Basic/Structure_of_matter_and_thermodynamics/Images/equilibrium_neutr.tex @@ -1,5 +1,5 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} \begin{document} \begin{tikzpicture} diff --git a/Physics/Basic/Structure_of_matter_and_thermodynamics/Images/equilibrium_stab.pdf b/Physics/Basic/Structure_of_matter_and_thermodynamics/Images/equilibrium_stab.pdf index f192ecc..ee456e7 100644 Binary files a/Physics/Basic/Structure_of_matter_and_thermodynamics/Images/equilibrium_stab.pdf and b/Physics/Basic/Structure_of_matter_and_thermodynamics/Images/equilibrium_stab.pdf differ diff --git a/Physics/Basic/Structure_of_matter_and_thermodynamics/Images/equilibrium_stab.tex b/Physics/Basic/Structure_of_matter_and_thermodynamics/Images/equilibrium_stab.tex index e4a6091..af16477 100644 --- a/Physics/Basic/Structure_of_matter_and_thermodynamics/Images/equilibrium_stab.tex +++ b/Physics/Basic/Structure_of_matter_and_thermodynamics/Images/equilibrium_stab.tex @@ -1,5 +1,5 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} \begin{document} \begin{tikzpicture} diff --git a/Physics/Basic/Structure_of_matter_and_thermodynamics/Images/equilibrium_unstab.pdf b/Physics/Basic/Structure_of_matter_and_thermodynamics/Images/equilibrium_unstab.pdf index 7ec7380..8dd7afb 100644 Binary files a/Physics/Basic/Structure_of_matter_and_thermodynamics/Images/equilibrium_unstab.pdf and b/Physics/Basic/Structure_of_matter_and_thermodynamics/Images/equilibrium_unstab.pdf differ diff --git a/Physics/Basic/Structure_of_matter_and_thermodynamics/Images/equilibrium_unstab.tex b/Physics/Basic/Structure_of_matter_and_thermodynamics/Images/equilibrium_unstab.tex index 546cba0..7c356e3 100644 --- a/Physics/Basic/Structure_of_matter_and_thermodynamics/Images/equilibrium_unstab.tex +++ b/Physics/Basic/Structure_of_matter_and_thermodynamics/Images/equilibrium_unstab.tex @@ -1,5 +1,5 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} \begin{document} \begin{tikzpicture} diff --git a/Physics/Basic/Structure_of_matter_and_thermodynamics/Images/fermi.pdf b/Physics/Basic/Structure_of_matter_and_thermodynamics/Images/fermi.pdf index c9e519b..ca7132d 100644 Binary files a/Physics/Basic/Structure_of_matter_and_thermodynamics/Images/fermi.pdf and b/Physics/Basic/Structure_of_matter_and_thermodynamics/Images/fermi.pdf differ diff --git a/Physics/Basic/Structure_of_matter_and_thermodynamics/Images/fermi.tex b/Physics/Basic/Structure_of_matter_and_thermodynamics/Images/fermi.tex index 8079e7d..5fd6813 100644 --- a/Physics/Basic/Structure_of_matter_and_thermodynamics/Images/fermi.tex +++ b/Physics/Basic/Structure_of_matter_and_thermodynamics/Images/fermi.tex @@ -1,5 +1,6 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} +\usepackage{../../../../preamble_math} \begin{document} \begin{tikzpicture} diff --git a/Physics/Basic/Structure_of_matter_and_thermodynamics/Images/heat_engine.pdf b/Physics/Basic/Structure_of_matter_and_thermodynamics/Images/heat_engine.pdf index c6eb4e0..c73ceff 100644 Binary files a/Physics/Basic/Structure_of_matter_and_thermodynamics/Images/heat_engine.pdf and b/Physics/Basic/Structure_of_matter_and_thermodynamics/Images/heat_engine.pdf differ diff --git a/Physics/Basic/Structure_of_matter_and_thermodynamics/Images/heat_engine.tex b/Physics/Basic/Structure_of_matter_and_thermodynamics/Images/heat_engine.tex index 836ea92..8756f58 100644 --- a/Physics/Basic/Structure_of_matter_and_thermodynamics/Images/heat_engine.tex +++ b/Physics/Basic/Structure_of_matter_and_thermodynamics/Images/heat_engine.tex @@ -1,5 +1,6 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} +\usepackage{../../../../preamble_math} \begin{document} \begin{tikzpicture} diff --git a/Physics/Basic/Structure_of_matter_and_thermodynamics/Images/heat_pump.pdf b/Physics/Basic/Structure_of_matter_and_thermodynamics/Images/heat_pump.pdf index 1f46f88..1b068e9 100644 Binary files a/Physics/Basic/Structure_of_matter_and_thermodynamics/Images/heat_pump.pdf and b/Physics/Basic/Structure_of_matter_and_thermodynamics/Images/heat_pump.pdf differ diff --git a/Physics/Basic/Structure_of_matter_and_thermodynamics/Images/heat_pump.tex b/Physics/Basic/Structure_of_matter_and_thermodynamics/Images/heat_pump.tex index e7dd5de..a9b3a0e 100644 --- a/Physics/Basic/Structure_of_matter_and_thermodynamics/Images/heat_pump.tex +++ b/Physics/Basic/Structure_of_matter_and_thermodynamics/Images/heat_pump.tex @@ -1,5 +1,6 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} +\usepackage{../../../../preamble_math} \begin{document} \begin{tikzpicture} diff --git a/Physics/Basic/Structure_of_matter_and_thermodynamics/Images/standard_model.pdf b/Physics/Basic/Structure_of_matter_and_thermodynamics/Images/standard_model.pdf index 57f6a51..1204825 100644 Binary files a/Physics/Basic/Structure_of_matter_and_thermodynamics/Images/standard_model.pdf and b/Physics/Basic/Structure_of_matter_and_thermodynamics/Images/standard_model.pdf differ diff --git a/Physics/Basic/Structure_of_matter_and_thermodynamics/Images/standard_model.tex b/Physics/Basic/Structure_of_matter_and_thermodynamics/Images/standard_model.tex index ee83775..df0bfe6 100644 --- a/Physics/Basic/Structure_of_matter_and_thermodynamics/Images/standard_model.tex +++ b/Physics/Basic/Structure_of_matter_and_thermodynamics/Images/standard_model.tex @@ -1,5 +1,5 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} \begin{document} \begin{tikzpicture} diff --git a/Physics/Basic/Structure_of_matter_and_thermodynamics/Images/thorium_series.pdf b/Physics/Basic/Structure_of_matter_and_thermodynamics/Images/thorium_series.pdf index 058c8cb..d48ceec 100644 Binary files a/Physics/Basic/Structure_of_matter_and_thermodynamics/Images/thorium_series.pdf and b/Physics/Basic/Structure_of_matter_and_thermodynamics/Images/thorium_series.pdf differ diff --git a/Physics/Basic/Structure_of_matter_and_thermodynamics/Images/thorium_series.tex b/Physics/Basic/Structure_of_matter_and_thermodynamics/Images/thorium_series.tex index a9b8e6d..a8950ca 100644 --- a/Physics/Basic/Structure_of_matter_and_thermodynamics/Images/thorium_series.tex +++ b/Physics/Basic/Structure_of_matter_and_thermodynamics/Images/thorium_series.tex @@ -1,5 +1,5 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} \begin{document} \begin{tikzpicture} diff --git a/Physics/Basic/Structure_of_matter_and_thermodynamics/Images/ultraviolet_catastrophe.pdf b/Physics/Basic/Structure_of_matter_and_thermodynamics/Images/ultraviolet_catastrophe.pdf index da4482a..bc48620 100644 Binary files a/Physics/Basic/Structure_of_matter_and_thermodynamics/Images/ultraviolet_catastrophe.pdf and b/Physics/Basic/Structure_of_matter_and_thermodynamics/Images/ultraviolet_catastrophe.pdf differ diff --git a/Physics/Basic/Structure_of_matter_and_thermodynamics/Images/ultraviolet_catastrophe.tex b/Physics/Basic/Structure_of_matter_and_thermodynamics/Images/ultraviolet_catastrophe.tex index 834f0db..84cabc6 100644 --- a/Physics/Basic/Structure_of_matter_and_thermodynamics/Images/ultraviolet_catastrophe.tex +++ b/Physics/Basic/Structure_of_matter_and_thermodynamics/Images/ultraviolet_catastrophe.tex @@ -1,37 +1,38 @@ \documentclass{standalone} -\usepackage{../../../../preamble_formulas} +\usepackage{../../../../preamble_tikz} +\usepackage{../../../../preamble_math} \begin{document} \begin{tikzpicture} - \def\c{299792458} - \def\h{6.626070*10^(-34)} - \def\kb{1.380649*10^(-23)} - \begin{axis}[ - width=12.5cm, - height=10cm, - xmin = 1e-7, - xmax = 3e-6, - %xtick distance = 0.001, - ymin = -1e10, - ymax = 5e13, - % axis equal image, - ylabel={Spectral radiance [$\text{W}\cdot\text{m}^{-3}$]}, - xlabel={Wavelength [m]}, - legend cell align = {left}, % - legend style={at={(axis cs:2.94e-6,4.5e13)},anchor=north east} % position of the legend box and anchor is the point on the box to be fitted exactly at the point of cs:<>,<>. Options are anchor=center,south west,south east,north west,north east,north,south,west... - ] - \shade[shading=rainbow,shading angle=90,opacity=0.3] (axis cs:400e-9,0) rectangle (axis cs:700e-9,5e13); - \node[font=\tiny, black!50] at (axis cs: 300e-9,4.78e13) {\textbf{UV}}; - \node[font=\tiny, black!50] at (axis cs: 550e-9,4.78e13) {\textbf{VISIBLE}}; - \node[font=\tiny, black!50] at (axis cs: 1850e-9,4.78e13) {\textbf{INFRARED}}; + \def\c{299792458} + \def\h{6.626070*10^(-34)} + \def\kb{1.380649*10^(-23)} + \begin{axis}[ + width=12.5cm, + height=10cm, + xmin = 1e-7, + xmax = 3e-6, + %xtick distance = 0.001, + ymin = -1e10, + ymax = 5e13, + % axis equal image, + ylabel={Spectral radiance [$\text{W}\cdot\text{m}^{-3}$]}, + xlabel={Wavelength [m]}, + legend cell align = {left}, % + legend style={at={(axis cs:2.94e-6,4.5e13)},anchor=north east} % position of the legend box and anchor is the point on the box to be fitted exactly at the point of cs:<>,<>. Options are anchor=center,south west,south east,north west,north east,north,south,west... + ] + \shade[shading=rainbow,shading angle=90,opacity=0.3] (axis cs:400e-9,0) rectangle (axis cs:700e-9,5e13); + \node[font=\tiny, black!50] at (axis cs: 300e-9,4.78e13) {\textbf{UV}}; + \node[font=\tiny, black!50] at (axis cs: 550e-9,4.78e13) {\textbf{VISIBLE}}; + \node[font=\tiny, black!50] at (axis cs: 1850e-9,4.78e13) {\textbf{INFRARED}}; - % Planck - \addplot [thin,samples=200,smooth,blue,domain=1e-7:3e-6] {2*pi*\h*\c*\c/(x^5*(e^(\h*\c/(x*\kb*5000))-1))}; % 5000 K - \addplot [thin,samples=200,smooth,color_green2,domain=1e-7:3e-6] {2*pi*\h*\c*\c/(x^5*(e^(\h*\c/(x*\kb*4000))-1))}; % 4000 K - \addplot [thin,samples=200,smooth,red,domain=1e-7:3e-6] {2*pi*\h*\c*\c/(x^5*(e^(\h*\c/(x*\kb*3000))-1))}; % 3000 K - % Rayleigh-Jeans - \addplot [thin,samples=200,smooth,black,domain=1.25e-6:3e-6] {2*pi*\c*\kb*5000/x^4}; % 5000 K - \legend{5000 K - Planck,4000 K - Planck,3000 K - Planck,5000 K - Rayleigh-Jeans} - \end{axis} + % Planck + \addplot [thin,samples=200,smooth,blue,domain=1e-7:3e-6] {2*pi*\h*\c*\c/(x^5*(e^(\h*\c/(x*\kb*5000))-1))}; % 5000 K + \addplot [thin,samples=200,smooth,color_green2,domain=1e-7:3e-6] {2*pi*\h*\c*\c/(x^5*(e^(\h*\c/(x*\kb*4000))-1))}; % 4000 K + \addplot [thin,samples=200,smooth,red,domain=1e-7:3e-6] {2*pi*\h*\c*\c/(x^5*(e^(\h*\c/(x*\kb*3000))-1))}; % 3000 K + % Rayleigh-Jeans + \addplot [thin,samples=200,smooth,black,domain=1.25e-6:3e-6] {2*pi*\c*\kb*5000/x^4}; % 5000 K + \legend{5000 K - Planck,4000 K - Planck,3000 K - Planck,5000 K - Rayleigh-Jeans} + \end{axis} \end{tikzpicture} \end{document} \ No newline at end of file diff --git a/main_math.idx b/main_math.idx index 9112fa2..cb3b813 100644 --- a/main_math.idx +++ b/main_math.idx @@ -1004,6 +1004,7 @@ \indexentry{Newton's divided differences\\method|hyperpage}{93} \indexentry{equally-spaced|hyperpage}{93} \indexentry{Hermite interpolation problem|hyperpage}{94} +\indexentry{Runge's phenomenon|hyperpage}{94} \indexentry{Spline|hyperpage}{94} \indexentry{spline|hyperpage}{94} \indexentry{cubic splines|hyperpage}{94} @@ -2945,10 +2946,6 @@ \indexentry{Riesz representation theorem|hyperpage}{312} \indexentry{adjoint operator|hyperpage}{312} \indexentry{self-adjoint|hyperpage}{312} -\indexentry{continuous|hyperpage}{313} -\indexentry{coercive|hyperpage}{313} -\indexentry{symmetric|hyperpage}{313} -\indexentry{Lax-Milgram theorem|hyperpage}{313} \indexentry{orthogonal system|hyperpage}{313} \indexentry{orthonormal system|hyperpage}{313} \indexentry{complete|hyperpage}{313} @@ -2961,7 +2958,7 @@ \indexentry{Fourier transform|hyperpage}{313} \indexentry{Riesz-Fischer theorem|hyperpage}{313} \indexentry{Parseval identity|hyperpage}{313} -\indexentry{Spectral theorem|hyperpage}{314} +\indexentry{Spectral theorem|hyperpage}{313} \indexentry{Hilbert-Schmidt spectral representation theorem|hyperpage}{314} \indexentry{Fredholm alternative|hyperpage}{314} \indexentry{Law of total probability|hyperpage}{315} @@ -3087,245 +3084,282 @@ \indexentry{rotation number|hyperpage}{338} \indexentry{semi-conjugate|hyperpage}{338} \indexentry{conjugate|hyperpage}{338} -\indexentry{measure on $\mathcal {C}(\ensuremath {\mathbb {T}}^1)$|hyperpage}{338} -\indexentry{probability measure|hyperpage}{338} -\indexentry{pushforward measure|hyperpage}{339} +\indexentry{measure on $\mathcal {C}(\ensuremath {\mathbb {T}}^1)$|hyperpage}{339} +\indexentry{probability measure|hyperpage}{339} +\indexentry{push-forward measure|hyperpage}{339} \indexentry{invariant|hyperpage}{339} \indexentry{$F$-invariant|hyperpage}{339} -\indexentry{$\sigma $-algebra|hyperpage}{340} -\indexentry{$\sigma $-algebra|hyperpage}{340} -\indexentry{measurable space|hyperpage}{340} -\indexentry{$\sigma $-algebra generated by $\mathcal {F}$|hyperpage}{340} -\indexentry{measurable|hyperpage}{340} -\indexentry{Measure|hyperpage}{340} -\indexentry{measure|hyperpage}{340} -\indexentry{measure space|hyperpage}{340} -\indexentry{integral of $f$ with respect to $\mu $|hyperpage}{340} -\indexentry{integral of $f$ with respect to $\mu $|hyperpage}{340} -\indexentry{Monotone convergence theorem|hyperpage}{340} -\indexentry{Fatou's lemma|hyperpage}{340} -\indexentry{Dominated convergence theorem|hyperpage}{340} -\indexentry{Product measure|hyperpage}{340} -\indexentry{product measure|hyperpage}{340} -\indexentry{$\sigma $-finite|hyperpage}{340} -\indexentry{Fubini|hyperpage}{340} -\indexentry{density|hyperpage}{341} -\indexentry{absolutely continuous|hyperpage}{341} -\indexentry{Radon-Nikodym|hyperpage}{341} -\indexentry{probability space|hyperpage}{341} -\indexentry{events|hyperpage}{341} -\indexentry{Random variable|hyperpage}{341} -\indexentry{$E$-valued random variable|hyperpage}{341} -\indexentry{Expectation|hyperpage}{341} -\indexentry{expectation of $X$|hyperpage}{341} -\indexentry{law of $X$|hyperpage}{341} -\indexentry{$\sigma $-algebra generated by $X$|hyperpage}{341} -\indexentry{Jensen's inequality|hyperpage}{341} -\indexentry{conditional expectation of $X$ given $\mathcal {G}$|hyperpage}{341} -\indexentry{Tower property|hyperpage}{342} -\indexentry{conditional expectation of $X$ given $Y$|hyperpage}{342} -\indexentry{probability kernel|hyperpage}{342} -\indexentry{conditional law of $X$ given $Y$|hyperpage}{342} -\indexentry{filtration|hyperpage}{342} -\indexentry{filtered probability space|hyperpage}{342} -\indexentry{adapted|hyperpage}{342} -\indexentry{martingale|hyperpage}{342} -\indexentry{submartingale|hyperpage}{342} -\indexentry{supermartingale|hyperpage}{342} -\indexentry{stopping time|hyperpage}{342} -\indexentry{stopped process|hyperpage}{342} -\indexentry{uniformly integrable|hyperpage}{342} -\indexentry{converges weakly|hyperpage}{343} -\indexentry{converges strongly|hyperpage}{343} -\indexentry{converges weakly-*|hyperpage}{343} -\indexentry{Banach-Alaoglu theorem|hyperpage}{343} -\indexentry{strongly lower-semicontinuous|hyperpage}{343} -\indexentry{weakly lower-semicontinuity|hyperpage}{343} -\indexentry{weak-* lower-semicontinuity|hyperpage}{343} -\indexentry{support plane|hyperpage}{343} -\indexentry{Sobolev spaces|hyperpage}{344} -\indexentry{Sobolev spaces|hyperpage}{344} -\indexentry{Poincaré's inequality|hyperpage}{344} -\indexentry{Poincaré-Wirtinger's inequality|hyperpage}{344} -\indexentry{embedded|hyperpage}{345} -\indexentry{compactly embedded|hyperpage}{345} -\indexentry{Gagliardo, Nirengerg and Sobolev's inequality|hyperpage}{345} -\indexentry{Hölder continuity|hyperpage}{345} -\indexentry{$\mathcal {C}^{k,\theta }$-Hölder continuous|hyperpage}{345} -\indexentry{Morrey's embedding|hyperpage}{345} -\indexentry{extension|hyperpage}{345} -\indexentry{extension operator|hyperpage}{345} -\indexentry{first order reflection|hyperpage}{346} -\indexentry{Reillich-Kondrachov's compactness theorem|hyperpage}{346} -\indexentry{trace operator|hyperpage}{346} -\indexentry{Gradient descent algorithm|hyperpage}{347} -\indexentry{gradient descent algorithm|hyperpage}{347} -\indexentry{Armijo-type rule|hyperpage}{347} -\indexentry{Frank-Wolfe-type method|hyperpage}{347} -\indexentry{$L$-co-coercive|hyperpage}{347} -\indexentry{firmly non-expansive|hyperpage}{347} -\indexentry{Baillon-Haddad|hyperpage}{347} -\indexentry{strongly convex|hyperpage}{347} -\indexentry{$\gamma $-convex|hyperpage}{347} -\indexentry{Newton method|hyperpage}{348} -\indexentry{Newton method|hyperpage}{348} -\indexentry{multistep method|hyperpage}{348} -\indexentry{Heavy ball method|hyperpage}{348} -\indexentry{Conjugate gradient|hyperpage}{348} -\indexentry{conjugate gradient method|hyperpage}{348} -\indexentry{Nesterov's accelerated gradient method|hyperpage}{348} -\indexentry{Nesterov's method|hyperpage}{348} -\indexentry{subgradient descent method|hyperpage}{348} -\indexentry{implicit descent|hyperpage}{348} -\indexentry{nonexpansive|hyperpage}{348} -\indexentry{avergaed|hyperpage}{348} -\indexentry{Opial's lemma|hyperpage}{348} -\indexentry{Krasnoselskii-Mann's convergence theorem|hyperpage}{349} -\indexentry{linear second-order PDE|hyperpage}{350} -\indexentry{non-divergence form|hyperpage}{350} -\indexentry{divergence form|hyperpage}{350} -\indexentry{Dirichlet boundary condition|hyperpage}{350} -\indexentry{homogeneous|hyperpage}{350} -\indexentry{Neumann boundary condition|hyperpage}{350} -\indexentry{homogeneous|hyperpage}{350} -\indexentry{uniformly elliptic|hyperpage}{350} -\indexentry{Abstract Fredholm alternative|hyperpage}{350} -\indexentry{weak formulation|hyperpage}{350} -\indexentry{formal adjoint|hyperpage}{350} -\indexentry{homogeneous adjoint problem|hyperpage}{350} -\indexentry{resolvent set|hyperpage}{351} -\indexentry{spectrum|hyperpage}{351} -\indexentry{Inner regularity|hyperpage}{351} -\indexentry{Regularity up to the boundary|hyperpage}{351} -\indexentry{Weak maximum principle|hyperpage}{351} -\indexentry{Weak maximum principle|hyperpage}{351} -\indexentry{strong solution|hyperpage}{352} -\indexentry{classical solution|hyperpage}{352} -\indexentry{Weak maximum principle|hyperpage}{352} -\indexentry{Hopf's lemma|hyperpage}{352} -\indexentry{interior ball condition|hyperpage}{352} -\indexentry{Strong maximum principle|hyperpage}{352} -\indexentry{Continuation method|hyperpage}{352} -\indexentry{Brower fixed point|hyperpage}{353} -\indexentry{Schauder fixed point|hyperpage}{353} -\indexentry{Schaefer fixed point|hyperpage}{353} -\indexentry{Montecarlo estimator|hyperpage}{354} -\indexentry{seed|hyperpage}{354} -\indexentry{Mersenne Twister algorithm|hyperpage}{354} -\indexentry{Acceptance-rejection method|hyperpage}{354} -\indexentry{Box-Muller method|hyperpage}{355} -\indexentry{Polar method|hyperpage}{355} -\indexentry{antithetic method|hyperpage}{355} -\indexentry{control variate|hyperpage}{355} -\indexentry{multiple control variate estimator|hyperpage}{356} -\indexentry{equivalent|hyperpage}{356} -\indexentry{importance sampling estimator|hyperpage}{356} -\indexentry{Euler method|hyperpage}{357} -\indexentry{continuous Euler scheme|hyperpage}{357} -\indexentry{Strong error of the Euler scheme|hyperpage}{357} -\indexentry{Weak error of the Euler scheme|hyperpage}{357} -\indexentry{Romberg Extrapolation|hyperpage}{357} -\indexentry{Romberg Extrapolation|hyperpage}{357} -\indexentry{Dirichlet boundary conditions|hyperpage}{359} -\indexentry{Neumann boundary conditions|hyperpage}{359} -\indexentry{Robin boundary conditions|hyperpage}{359} -\indexentry{conforming Galerkin method|hyperpage}{359} -\indexentry{Céa's lemma|hyperpage}{359} -\indexentry{finite element|hyperpage}{359} -\indexentry{basis functions|hyperpage}{360} -\indexentry{local interpolant|hyperpage}{360} -\indexentry{subdivision|hyperpage}{360} -\indexentry{global interpolant|hyperpage}{360} -\indexentry{triangulation|hyperpage}{360} -\indexentry{affinely equivalent|hyperpage}{360} -\indexentry{Bramble-Hilbert lemma|hyperpage}{360} -\indexentry{diameter|hyperpage}{360} -\indexentry{insphere diameter|hyperpage}{360} -\indexentry{condition number|hyperpage}{360} -\indexentry{Local interpolation error|hyperpage}{361} -\indexentry{regular|hyperpage}{361} -\indexentry{Global interpolation error|hyperpage}{361} -\indexentry{spectral methods|hyperpage}{361} -\indexentry{trial functions|hyperpage}{361} -\indexentry{globally smooth|hyperpage}{361} -\indexentry{Galerkin methods|hyperpage}{361} -\indexentry{Collocation methods|hyperpage}{361} -\indexentry{collocation points|hyperpage}{361} -\indexentry{$\tau $ methods|hyperpage}{361} -\indexentry{interpolant|hyperpage}{361} -\indexentry{Runge phenomenon|hyperpage}{362} -\indexentry{Chebyshev polynomials|hyperpage}{362} -\indexentry{interpolant|hyperpage}{362} -\indexentry{jointly Gaussian|hyperpage}{363} -\indexentry{Brownian motion|hyperpage}{363} -\indexentry{Strong law of large numbers for Brownian motion|hyperpage}{363} -\indexentry{Markov property for Brownian motion|hyperpage}{363} -\indexentry{natural filtration|hyperpage}{363} -\indexentry{Martingale|hyperpage}{363} -\indexentry{martingale|hyperpage}{363} -\indexentry{adapted|hyperpage}{363} -\indexentry{sub-martingale|hyperpage}{363} -\indexentry{super-martingale|hyperpage}{363} -\indexentry{hitting time|hyperpage}{364} -\indexentry{Doob's optional sampling theorem|hyperpage}{364} -\indexentry{stopped process|hyperpage}{364} -\indexentry{Orthogonality of martingales|hyperpage}{364} -\indexentry{Doob's maximal inequality|hyperpage}{364} -\indexentry{absoulte variation|hyperpage}{364} -\indexentry{finite variation|hyperpage}{364} -\indexentry{Quadratic variation|hyperpage}{364} -\indexentry{mesh|hyperpage}{364} -\indexentry{continuous local martingale|hyperpage}{365} -\indexentry{localizing sequence|hyperpage}{365} -\indexentry{Doob's optional sampling theorem for local martingales|hyperpage}{365} -\indexentry{Levy's characterization of Brownian motion|hyperpage}{366} -\indexentry{isometry|hyperpage}{366} -\indexentry{partial isometry|hyperpage}{366} -\indexentry{Wiener integral|hyperpage}{366} -\indexentry{Wiener isometry|hyperpage}{366} -\indexentry{Wiener integral|hyperpage}{366} -\indexentry{Wiener integral|hyperpage}{366} -\indexentry{Chasles relation|hyperpage}{366} -\indexentry{progressive|hyperpage}{367} -\indexentry{Itô integral|hyperpage}{368} -\indexentry{Itô isometry|hyperpage}{368} -\indexentry{Itô integral|hyperpage}{368} -\indexentry{generalized Itô integral|hyperpage}{368} -\indexentry{Stochastic dominated convergence theorem|hyperpage}{368} -\indexentry{Itô process|hyperpage}{369} -\indexentry{martingale term|hyperpage}{369} -\indexentry{drift term|hyperpage}{369} -\indexentry{stochastic differential|hyperpage}{369} -\indexentry{quadratic variation|hyperpage}{369} -\indexentry{Stochastic integration by parts|hyperpage}{370} -\indexentry{Itô term|hyperpage}{370} -\indexentry{Itô's formula|hyperpage}{370} -\indexentry{Doléans-Dade exponential|hyperpage}{370} -\indexentry{Novikov's condition|hyperpage}{370} -\indexentry{Giranov's theorem|hyperpage}{371} -\indexentry{drift|hyperpage}{371} -\indexentry{diffusion|hyperpage}{371} -\indexentry{stochastic differential equation|hyperpage}{371} -\indexentry{SDE|hyperpage}{371} -\indexentry{solution of the SDE|hyperpage}{371} -\indexentry{Gronwall's lemma|hyperpage}{371} -\indexentry{Existence and uniqueness of solutions of SDEs|hyperpage}{371} -\indexentry{Langevin equation|hyperpage}{371} -\indexentry{Geometric Brownian motion|hyperpage}{372} -\indexentry{Black-Scholes process|hyperpage}{372} -\indexentry{homogeneous SDE|hyperpage}{372} -\indexentry{diffusions|hyperpage}{372} -\indexentry{Invariance under time shift|hyperpage}{372} -\indexentry{Generator|hyperpage}{372} -\indexentry{generator|hyperpage}{372} -\indexentry{Kolmogorov's equation|hyperpage}{372} -\indexentry{Feynman-Kac's formula|hyperpage}{373} -\indexentry{Itô's formula|hyperpage}{374} -\indexentry{Flow property|hyperpage}{374} -\indexentry{Dynamic programming principle|hyperpage}{374} -\indexentry{Fokker-Planck equation|hyperpage}{374} -\indexentry{control parameter|hyperpage}{375} -\indexentry{Finite horizon problem|hyperpage}{375} -\indexentry{running cost|hyperpage}{375} -\indexentry{terminal cost|hyperpage}{375} -\indexentry{Infinte horizon problem|hyperpage}{375} +\indexentry{orbit|hyperpage}{339} +\indexentry{positive orbit|hyperpage}{339} +\indexentry{negative orbit|hyperpage}{339} +\indexentry{positively invariant|hyperpage}{340} +\indexentry{negatively invariant|hyperpage}{340} +\indexentry{invariant|hyperpage}{340} +\indexentry{positively recurrent points|hyperpage}{340} +\indexentry{negatively recurrent points|hyperpage}{340} +\indexentry{wandering point|hyperpage}{340} +\indexentry{wandering domain|hyperpage}{340} +\indexentry{non-wandering|hyperpage}{340} +\indexentry{minimal|hyperpage}{340} +\indexentry{minimal|hyperpage}{340} +\indexentry{measure of $U$|hyperpage}{340} +\indexentry{measure of $A$|hyperpage}{340} +\indexentry{support of $\mu $|hyperpage}{340} +\indexentry{Cantor set|hyperpage}{341} +\indexentry{uniquely ergodic|hyperpage}{341} +\indexentry{bounded variation|hyperpage}{342} +\indexentry{Denjoy-Koksma inequality|hyperpage}{342} +\indexentry{Denjoy theorem|hyperpage}{343} +\indexentry{$\sigma $-algebra|hyperpage}{344} +\indexentry{$\sigma $-algebra|hyperpage}{344} +\indexentry{measurable space|hyperpage}{344} +\indexentry{$\sigma $-algebra generated by $\mathcal {F}$|hyperpage}{344} +\indexentry{measurable|hyperpage}{344} +\indexentry{Measure|hyperpage}{344} +\indexentry{measure|hyperpage}{344} +\indexentry{measure space|hyperpage}{344} +\indexentry{integral of $f$ with respect to $\mu $|hyperpage}{344} +\indexentry{integral of $f$ with respect to $\mu $|hyperpage}{344} +\indexentry{Monotone convergence theorem|hyperpage}{344} +\indexentry{Fatou's lemma|hyperpage}{344} +\indexentry{Dominated convergence theorem|hyperpage}{344} +\indexentry{Product measure|hyperpage}{344} +\indexentry{product measure|hyperpage}{344} +\indexentry{$\sigma $-finite|hyperpage}{344} +\indexentry{Fubini|hyperpage}{344} +\indexentry{density|hyperpage}{345} +\indexentry{absolutely continuous|hyperpage}{345} +\indexentry{Radon-Nikodym|hyperpage}{345} +\indexentry{probability space|hyperpage}{345} +\indexentry{events|hyperpage}{345} +\indexentry{Random variable|hyperpage}{345} +\indexentry{$E$-valued random variable|hyperpage}{345} +\indexentry{Expectation|hyperpage}{345} +\indexentry{expectation of $X$|hyperpage}{345} +\indexentry{law of $X$|hyperpage}{345} +\indexentry{$\sigma $-algebra generated by $X$|hyperpage}{345} +\indexentry{Jensen's inequality|hyperpage}{345} +\indexentry{conditional expectation of $X$ given $\mathcal {G}$|hyperpage}{345} +\indexentry{Tower property|hyperpage}{346} +\indexentry{conditional expectation of $X$ given $Y$|hyperpage}{346} +\indexentry{probability kernel|hyperpage}{346} +\indexentry{conditional law of $X$ given $Y$|hyperpage}{346} +\indexentry{filtration|hyperpage}{346} +\indexentry{filtered probability space|hyperpage}{346} +\indexentry{adapted|hyperpage}{346} +\indexentry{martingale|hyperpage}{346} +\indexentry{submartingale|hyperpage}{346} +\indexentry{supermartingale|hyperpage}{346} +\indexentry{stopping time|hyperpage}{346} +\indexentry{stopped process|hyperpage}{346} +\indexentry{uniformly integrable|hyperpage}{346} +\indexentry{converges weakly|hyperpage}{347} +\indexentry{converges strongly|hyperpage}{347} +\indexentry{converges weakly-*|hyperpage}{347} +\indexentry{Banach-Alaoglu theorem|hyperpage}{347} +\indexentry{strongly lower-semicontinuous|hyperpage}{347} +\indexentry{weakly lower-semicontinuity|hyperpage}{347} +\indexentry{weak-* lower-semicontinuity|hyperpage}{347} +\indexentry{support plane|hyperpage}{347} +\indexentry{Sobolev spaces|hyperpage}{348} +\indexentry{Sobolev spaces|hyperpage}{348} +\indexentry{Poincaré's inequality|hyperpage}{348} +\indexentry{Poincaré-Wirtinger's inequality|hyperpage}{348} +\indexentry{embedded|hyperpage}{349} +\indexentry{compactly embedded|hyperpage}{349} +\indexentry{Gagliardo, Nirengerg and Sobolev's inequality|hyperpage}{349} +\indexentry{Hölder continuity|hyperpage}{349} +\indexentry{$\mathcal {C}^{k,\theta }$-Hölder continuous|hyperpage}{349} +\indexentry{Morrey's embedding|hyperpage}{349} +\indexentry{extension|hyperpage}{349} +\indexentry{extension operator|hyperpage}{349} +\indexentry{first order reflection|hyperpage}{350} +\indexentry{Reillich-Kondrachov's compactness theorem|hyperpage}{350} +\indexentry{trace operator|hyperpage}{350} +\indexentry{Gradient descent algorithm|hyperpage}{351} +\indexentry{gradient descent algorithm|hyperpage}{351} +\indexentry{Armijo-type rule|hyperpage}{351} +\indexentry{Frank-Wolfe-type method|hyperpage}{351} +\indexentry{$L$-co-coercive|hyperpage}{351} +\indexentry{firmly non-expansive|hyperpage}{351} +\indexentry{Baillon-Haddad|hyperpage}{351} +\indexentry{strongly convex|hyperpage}{351} +\indexentry{$\gamma $-convex|hyperpage}{351} +\indexentry{Newton method|hyperpage}{352} +\indexentry{Newton method|hyperpage}{352} +\indexentry{multistep method|hyperpage}{352} +\indexentry{Heavy ball method|hyperpage}{352} +\indexentry{Conjugate gradient|hyperpage}{352} +\indexentry{conjugate gradient method|hyperpage}{352} +\indexentry{Nesterov's accelerated gradient method|hyperpage}{352} +\indexentry{Nesterov's method|hyperpage}{352} +\indexentry{subgradient descent method|hyperpage}{352} +\indexentry{implicit descent|hyperpage}{352} +\indexentry{nonexpansive|hyperpage}{352} +\indexentry{avergaed|hyperpage}{352} +\indexentry{Opial's lemma|hyperpage}{352} +\indexentry{Krasnoselskii-Mann's convergence theorem|hyperpage}{353} +\indexentry{linear second-order PDE|hyperpage}{354} +\indexentry{non-divergence form|hyperpage}{354} +\indexentry{divergence form|hyperpage}{354} +\indexentry{Dirichlet boundary condition|hyperpage}{354} +\indexentry{homogeneous|hyperpage}{354} +\indexentry{Neumann boundary condition|hyperpage}{354} +\indexentry{homogeneous|hyperpage}{354} +\indexentry{uniformly elliptic|hyperpage}{354} +\indexentry{weak formulation|hyperpage}{354} +\indexentry{variational formulation|hyperpage}{354} +\indexentry{weak solution|hyperpage}{354} +\indexentry{strong solution|hyperpage}{354} +\indexentry{classical solution|hyperpage}{354} +\indexentry{continuous|hyperpage}{354} +\indexentry{coercive|hyperpage}{354} +\indexentry{symmetric|hyperpage}{354} +\indexentry{Lax-Milgram theorem|hyperpage}{355} +\indexentry{Abstract Fredholm alternative|hyperpage}{356} +\indexentry{formal adjoint|hyperpage}{356} +\indexentry{homogeneous adjoint problem|hyperpage}{356} +\indexentry{resolvent set|hyperpage}{356} +\indexentry{spectrum|hyperpage}{356} +\indexentry{Inner regularity|hyperpage}{357} +\indexentry{Regularity up to the boundary|hyperpage}{357} +\indexentry{Weak maximum principle|hyperpage}{357} +\indexentry{Weak maximum principle|hyperpage}{358} +\indexentry{Weak maximum principle|hyperpage}{358} +\indexentry{Hopf's lemma|hyperpage}{358} +\indexentry{interior ball condition|hyperpage}{358} +\indexentry{Strong maximum principle|hyperpage}{358} +\indexentry{Continuation method|hyperpage}{359} +\indexentry{Brower fixed point|hyperpage}{359} +\indexentry{Schauder fixed point|hyperpage}{359} +\indexentry{Schaefer fixed point|hyperpage}{359} +\indexentry{Montecarlo estimator|hyperpage}{360} +\indexentry{seed|hyperpage}{360} +\indexentry{Mersenne Twister algorithm|hyperpage}{360} +\indexentry{Acceptance-rejection method|hyperpage}{360} +\indexentry{Box-Muller method|hyperpage}{361} +\indexentry{Polar method|hyperpage}{361} +\indexentry{antithetic method|hyperpage}{361} +\indexentry{control variate|hyperpage}{361} +\indexentry{multiple control variate estimator|hyperpage}{362} +\indexentry{equivalent|hyperpage}{362} +\indexentry{importance sampling estimator|hyperpage}{362} +\indexentry{Euler method|hyperpage}{363} +\indexentry{continuous Euler scheme|hyperpage}{363} +\indexentry{Strong error of the Euler scheme|hyperpage}{363} +\indexentry{Weak error of the Euler scheme|hyperpage}{363} +\indexentry{Romberg Extrapolation|hyperpage}{363} +\indexentry{Romberg Extrapolation|hyperpage}{363} +\indexentry{finite difference estimator|hyperpage}{364} +\indexentry{Black-Scholes model|hyperpage}{364} +\indexentry{tangent process|hyperpage}{364} +\indexentry{price of an American option|hyperpage}{365} +\indexentry{risk-free interest rate|hyperpage}{365} +\indexentry{discretization method|hyperpage}{365} +\indexentry{naive approach|hyperpage}{365} +\indexentry{Tsitsiklis-Van Roy method|hyperpage}{365} +\indexentry{Tsitsiklis-Van Roy method|hyperpage}{365} +\indexentry{Longstaff-Schwartz method|hyperpage}{366} +\indexentry{Longstaff-Schwartz method|hyperpage}{366} +\indexentry{Rogers's lemma|hyperpage}{366} +\indexentry{Dirichlet boundary conditions|hyperpage}{367} +\indexentry{Neumann boundary conditions|hyperpage}{367} +\indexentry{Robin boundary conditions|hyperpage}{367} +\indexentry{conforming Galerkin method|hyperpage}{367} +\indexentry{Céa's lemma|hyperpage}{367} +\indexentry{finite element|hyperpage}{367} +\indexentry{basis functions|hyperpage}{368} +\indexentry{local interpolant|hyperpage}{368} +\indexentry{subdivision|hyperpage}{368} +\indexentry{global interpolant|hyperpage}{368} +\indexentry{triangulation|hyperpage}{368} +\indexentry{affinely equivalent|hyperpage}{368} +\indexentry{Bramble-Hilbert lemma|hyperpage}{368} +\indexentry{diameter|hyperpage}{368} +\indexentry{insphere diameter|hyperpage}{368} +\indexentry{condition number|hyperpage}{368} +\indexentry{Local interpolation error|hyperpage}{369} +\indexentry{regular|hyperpage}{369} +\indexentry{Global interpolation error|hyperpage}{369} +\indexentry{spectral methods|hyperpage}{369} +\indexentry{trial functions|hyperpage}{369} +\indexentry{globally smooth|hyperpage}{369} +\indexentry{Galerkin methods|hyperpage}{369} +\indexentry{Collocation methods|hyperpage}{369} +\indexentry{collocation points|hyperpage}{369} +\indexentry{$\tau $ methods|hyperpage}{369} +\indexentry{interpolant|hyperpage}{369} +\indexentry{interpolant|hyperpage}{370} +\indexentry{jointly Gaussian|hyperpage}{371} +\indexentry{Brownian motion|hyperpage}{371} +\indexentry{Strong law of large numbers for Brownian motion|hyperpage}{371} +\indexentry{Markov property for Brownian motion|hyperpage}{371} +\indexentry{natural filtration|hyperpage}{371} +\indexentry{Martingale|hyperpage}{371} +\indexentry{martingale|hyperpage}{371} +\indexentry{adapted|hyperpage}{371} +\indexentry{sub-martingale|hyperpage}{371} +\indexentry{super-martingale|hyperpage}{371} +\indexentry{hitting time|hyperpage}{372} +\indexentry{Doob's optional sampling theorem|hyperpage}{372} +\indexentry{stopped process|hyperpage}{372} +\indexentry{Orthogonality of martingales|hyperpage}{372} +\indexentry{Doob's maximal inequality|hyperpage}{372} +\indexentry{absoulte variation|hyperpage}{372} +\indexentry{finite variation|hyperpage}{372} +\indexentry{Quadratic variation|hyperpage}{372} +\indexentry{mesh|hyperpage}{372} +\indexentry{continuous local martingale|hyperpage}{373} +\indexentry{localizing sequence|hyperpage}{373} +\indexentry{Doob's optional sampling theorem for local martingales|hyperpage}{373} +\indexentry{Levy's characterization of Brownian motion|hyperpage}{374} +\indexentry{isometry|hyperpage}{374} +\indexentry{partial isometry|hyperpage}{374} +\indexentry{Wiener integral|hyperpage}{374} +\indexentry{Wiener isometry|hyperpage}{374} +\indexentry{Wiener integral|hyperpage}{374} +\indexentry{Wiener integral|hyperpage}{374} +\indexentry{Chasles relation|hyperpage}{374} +\indexentry{progressive|hyperpage}{375} +\indexentry{Itô integral|hyperpage}{376} +\indexentry{Itô isometry|hyperpage}{376} +\indexentry{Itô integral|hyperpage}{376} +\indexentry{generalized Itô integral|hyperpage}{376} +\indexentry{Stochastic dominated convergence theorem|hyperpage}{376} +\indexentry{Itô process|hyperpage}{377} +\indexentry{martingale term|hyperpage}{377} +\indexentry{drift term|hyperpage}{377} +\indexentry{stochastic differential|hyperpage}{377} +\indexentry{quadratic variation|hyperpage}{377} +\indexentry{Stochastic integration by parts|hyperpage}{378} +\indexentry{Itô term|hyperpage}{378} +\indexentry{Itô's formula|hyperpage}{378} +\indexentry{Doléans-Dade exponential|hyperpage}{378} +\indexentry{Novikov's condition|hyperpage}{378} +\indexentry{Giranov's theorem|hyperpage}{379} +\indexentry{drift|hyperpage}{379} +\indexentry{diffusion|hyperpage}{379} +\indexentry{stochastic differential equation|hyperpage}{379} +\indexentry{SDE|hyperpage}{379} +\indexentry{solution of the SDE|hyperpage}{379} +\indexentry{Gronwall's lemma|hyperpage}{379} +\indexentry{Existence and uniqueness of solutions of SDEs|hyperpage}{379} +\indexentry{Langevin equation|hyperpage}{379} +\indexentry{Geometric Brownian motion|hyperpage}{380} +\indexentry{Black-Scholes process|hyperpage}{380} +\indexentry{homogeneous SDE|hyperpage}{380} +\indexentry{diffusions|hyperpage}{380} +\indexentry{Invariance under time shift|hyperpage}{380} +\indexentry{Generator|hyperpage}{380} +\indexentry{generator|hyperpage}{380} +\indexentry{Kolmogorov's equation|hyperpage}{380} +\indexentry{Feynman-Kac's formula|hyperpage}{381} +\indexentry{Itô's formula|hyperpage}{382} +\indexentry{Flow property|hyperpage}{382} +\indexentry{Dynamic programming principle|hyperpage}{382} +\indexentry{Fokker-Planck equation|hyperpage}{382} +\indexentry{control parameter|hyperpage}{383} +\indexentry{Finite horizon problem|hyperpage}{383} +\indexentry{running cost|hyperpage}{383} +\indexentry{terminal cost|hyperpage}{383} +\indexentry{Infinte horizon problem|hyperpage}{383} diff --git a/main_math.ilg b/main_math.ilg index 887c781..0f87c9c 100644 --- a/main_math.ilg +++ b/main_math.ilg @@ -1,6 +1,6 @@ This is makeindex, version 2.17 [TeX Live 2023] (kpathsea + Thai support). -Scanning input file main_math.idx.......done (3331 entries accepted, 0 rejected). -Sorting entries...............................done (41166 comparisons). -Generating output file main_math.ind.......done (2842 lines written, 0 warnings). +Scanning input file main_math.idx.......done (3365 entries accepted, 0 rejected). +Sorting entries................................done (42220 comparisons). +Generating output file main_math.ind.......done (2868 lines written, 0 warnings). Output written in main_math.ind. Transcript written in main_math.ilg. diff --git a/main_math.ind b/main_math.ind index 19a8386..eeb866e 100644 --- a/main_math.ind +++ b/main_math.ind @@ -1,13 +1,13 @@ \begin{theindex} \item $(G,\cdot )$-space, \hyperpage{211} - \item $E$-valued random variable, \hyperpage{341} + \item $E$-valued random variable, \hyperpage{345} \item $F$-distribution with degrees of freedom $d_1$ and $d_2$, \hyperpage{252} \item $F$-invariant, \hyperpage{339} \item $F$-linearly independent, \hyperpage{170} \item $K$-field morphism, \hyperpage{165} - \item $L$-co-coercive, \hyperpage{347} + \item $L$-co-coercive, \hyperpage{351} \item $N$-th partial sum of $Sf$, \hyperpage{83} \item $N$-th partial sum of the series, \hyperpage{76}, \hyperpage{105} @@ -25,24 +25,24 @@ \item $\alpha $-limit set, \hyperpage{131} \item $\ensuremath {\mathbb {C}}$-differentiable, \hyperpage{109} \item $\ensuremath {\mathbb {R}}$-differentiable, \hyperpage{110} - \item $\gamma $-convex, \hyperpage{347} + \item $\gamma $-convex, \hyperpage{351} \item $\mathcal {C}^0$-close, \hyperpage{336} \item $\mathcal {C}^1$-close, \hyperpage{336} - \item $\mathcal {C}^{k,\theta }$-Hölder continuous, \hyperpage{345} + \item $\mathcal {C}^{k,\theta }$-Hölder continuous, \hyperpage{349} \item $\omega $-limit point, \hyperpage{131} \item $\omega $-limit set, \hyperpage{131} \item $\sigma $-additivity, \hyperpage{173}, \hyperpage{291} \item $\sigma $-algebra, \hyperpage{172}, \hyperpage{291}, - \hyperpage{340} + \hyperpage{344} \item $\sigma $-algebra generated, \hyperpage{172} - \item $\sigma $-algebra generated by $X$, \hyperpage{341} + \item $\sigma $-algebra generated by $X$, \hyperpage{345} \item $\sigma $-algebra generated by $\boldsymbol {\mathrm {X}}$, \hyperpage{321} - \item $\sigma $-algebra generated by $\mathcal {F}$, \hyperpage{340} + \item $\sigma $-algebra generated by $\mathcal {F}$, \hyperpage{344} \item $\sigma $-algebra of all Lebesgue measurable sets in $\ensuremath {\mathbb {R}}^n$, \hyperpage{175} - \item $\sigma $-finite, \hyperpage{340} - \item $\tau $ methods, \hyperpage{361} + \item $\sigma $-finite, \hyperpage{344} + \item $\tau $ methods, \hyperpage{369} \item $d$-dimensional standard Brownian motion, \hyperpage{332} \item $i$-th pivot, \hyperpage{14} \item $k$-linear map, \hyperpage{155} @@ -93,13 +93,13 @@ \item Absolute geometry, \hyperpage{64} \item absolute value, \hyperpage{25} \item absolutely continuous, \hyperpage{178}, \hyperpage{180}, - \hyperpage{341} + \hyperpage{345} \item absolutely convergent, \hyperpage{77}, \hyperpage{106}, \hyperpage{117}, \hyperpage{300} \item absolutely stable, \hyperpage{261} - \item absoulte variation, \hyperpage{364} - \item Abstract Fredholm alternative, \hyperpage{350} - \item Acceptance-rejection method, \hyperpage{354} + \item absoulte variation, \hyperpage{372} + \item Abstract Fredholm alternative, \hyperpage{356} + \item Acceptance-rejection method, \hyperpage{360} \item acceptation region, \hyperpage{199} \item ACCP, \hyperpage{46} \item accumulation point, \hyperpage{26}, \hyperpage{54} @@ -107,7 +107,7 @@ \item Adams method, \hyperpage{262} \item Adams-Bashforth method, \hyperpage{262} \item Adams-Moulton method, \hyperpage{262} - \item adapted, \hyperpage{342}, \hyperpage{363} + \item adapted, \hyperpage{346}, \hyperpage{371} \item adherence, \hyperpage{54} \item adherent point, \hyperpage{54}, \hyperpage{207} \item adjacency matrix, \hyperpage{50} @@ -122,7 +122,7 @@ \item affine plane, \hyperpage{66} \item affine space, \hyperpage{69} \item affine subvariety, \hyperpage{70} - \item affinely equivalent, \hyperpage{360} + \item affinely equivalent, \hyperpage{368} \item affinely independents, \hyperpage{69} \item affinity, \hyperpage{70} \item AIC, \hyperpage{257} @@ -155,7 +155,7 @@ \item angle-preserving, \hyperpage{149} \item anisotropic, \hyperpage{74} \item annihilator, \hyperpage{19} - \item antithetic method, \hyperpage{355} + \item antithetic method, \hyperpage{361} \item aperiodic, \hyperpage{320} \item approximation of identity, \hyperpage{79}, \hyperpage{241} \item approximations of the identity, \hyperpage{235} @@ -167,7 +167,7 @@ \item Archimedean property, \hyperpage{25} \item argument, \hyperpage{104} \item Argument principle, \hyperpage{118} - \item Armijo-type rule, \hyperpage{347} + \item Armijo-type rule, \hyperpage{351} \item Arnold family, \hyperpage{337} \item Artin's lemma, \hyperpage{169} \item Arzelà-Ascoli theorem, \hyperpage{121}, \hyperpage{125}, @@ -192,7 +192,7 @@ \item autonomous, \hyperpage{122} \item average, \hyperpage{289} \item average response, \hyperpage{253} - \item avergaed, \hyperpage{348} + \item avergaed, \hyperpage{352} \item Axiom of Archimedes, \hyperpage{63} \item Axiom of choice, \hyperpage{213} \item Axiom of completeness, \hyperpage{63} @@ -205,13 +205,13 @@ \item backward Euler method, \hyperpage{258} \item Backward-time central-space, \hyperpage{268}, \hyperpage{274} - \item Baillon-Haddad, \hyperpage{347} + \item Baillon-Haddad, \hyperpage{351} \item Baire's theorem, \hyperpage{309} \item balance equation, \hyperpage{329} \item ball, \hyperpage{205} \item Banach fixed-point theorem, \hyperpage{125} \item Banach space, \hyperpage{301} - \item Banach-Alaoglu theorem, \hyperpage{343} + \item Banach-Alaoglu theorem, \hyperpage{347} \item Banach-Steinhaus theorem, \hyperpage{310} \item bandlimited, \hyperpage{239} \item Barrow's law, \hyperpage{298} @@ -221,7 +221,7 @@ \item basic feasible solutions, \hyperpage{51} \item basin, \hyperpage{131} \item basis, \hyperpage{16}, \hyperpage{206} - \item basis functions, \hyperpage{360} + \item basis functions, \hyperpage{368} \item Bautin's theorem, \hyperpage{226} \item Bayes estimate, \hyperpage{203} \item Bayes' formula, \hyperpage{174} @@ -254,7 +254,8 @@ \item bipartite, \hyperpage{50} \item birth and death process, \hyperpage{329} \item Bisection method, \hyperpage{90} - \item Black-Scholes process, \hyperpage{372} + \item Black-Scholes model, \hyperpage{364} + \item Black-Scholes process, \hyperpage{380} \item block matrix, \hyperpage{15} \item blow-down, \hyperpage{225} \item Blow-up in cartesian coordinates, \hyperpage{226} @@ -283,14 +284,15 @@ \item bounded from above, \hyperpage{25, 26} \item bounded from below, \hyperpage{25, 26} \item bounded set, \hyperpage{54} + \item bounded variation, \hyperpage{342} \item box topology, \hyperpage{209} \item Box-Cox transformation, \hyperpage{257} - \item Box-Muller method, \hyperpage{355} - \item Bramble-Hilbert lemma, \hyperpage{360} + \item Box-Muller method, \hyperpage{361} + \item Bramble-Hilbert lemma, \hyperpage{368} \item bridge, \hyperpage{50} \item Brouwer's fixed-point theorem, \hyperpage{215} - \item Brower fixed point, \hyperpage{353} - \item Brownian motion, \hyperpage{330}, \hyperpage{363} + \item Brower fixed point, \hyperpage{359} + \item Brownian motion, \hyperpage{330}, \hyperpage{371} \item Broyden's method, \hyperpage{263} \item Broyden-Fletcher-Goldfarb-Shanno method, \hyperpage{264} \item BTCS, \hyperpage{268} @@ -306,7 +308,7 @@ \hyperpage{51} \item canonical form of a linear programming to minimize, \hyperpage{51} - \item Cantor set, \hyperpage{209} + \item Cantor set, \hyperpage{209}, \hyperpage{341} \item Cantor's theorem, \hyperpage{9} \item Cantor-Bernstein theorem, \hyperpage{9} \item Cardano-Vieta's formulas, \hyperpage{114} @@ -375,9 +377,9 @@ \item Characteristic function, \hyperpage{191} \item characteristic function, \hyperpage{9}, \hyperpage{191} \item characteristic polynomial, \hyperpage{20}, \hyperpage{49} - \item Chasles relation, \hyperpage{366} + \item Chasles relation, \hyperpage{374} \item Chebyshev method, \hyperpage{90} - \item Chebyshev polynomials, \hyperpage{96}, \hyperpage{362} + \item Chebyshev polynomials, \hyperpage{96} \item Chebyshev's inequality, \hyperpage{186}, \hyperpage{297} \item chi-squared distribution with $n$ degrees of freedom, \hyperpage{197} @@ -390,7 +392,7 @@ \item class $\mathcal {C}^n$ at a point $a\in \ensuremath {\mathbb {R}}$, \hyperpage{31} \item class $\mathcal {C}^p$, \hyperpage{31} - \item classical solution, \hyperpage{352} + \item classical solution, \hyperpage{354} \item Classification of affine quadrics, \hyperpage{75} \item Classification of compact connected surfaces, \hyperpage{219} \item Classification of connected 1-manifolds, \hyperpage{217} @@ -427,13 +429,13 @@ \item codimension, \hyperpage{223} \item coefficient of determination, \hyperpage{252} \item coefficients, \hyperpage{11} - \item coercive, \hyperpage{313} + \item coercive, \hyperpage{354} \item cofactor, \hyperpage{136} \item cofactor matrix, \hyperpage{15} \item Cofinite topology, \hyperpage{206} \item collineation, \hyperpage{66} - \item Collocation methods, \hyperpage{361} - \item collocation points, \hyperpage{361} + \item Collocation methods, \hyperpage{369} + \item collocation points, \hyperpage{369} \item column rank, \hyperpage{16} \item Combinations with repetition, \hyperpage{10} \item Combinations without repetition, \hyperpage{10} @@ -444,7 +446,7 @@ \item Compact space, \hyperpage{213} \item compact subset, \hyperpage{213} \item compact support, \hyperpage{79} - \item compactly embedded, \hyperpage{345} + \item compactly embedded, \hyperpage{349} \item compactness, \hyperpage{213} \item Comparison test, \hyperpage{76}, \hyperpage{80}, \hyperpage{183} @@ -483,13 +485,13 @@ \item computational efficiency, \hyperpage{91} \item concave, \hyperpage{30} \item Condensation test, \hyperpage{76} - \item condition number, \hyperpage{99}, \hyperpage{360} + \item condition number, \hyperpage{99}, \hyperpage{368} \item conditional consistency, \hyperpage{269} \item conditional expectation, \hyperpage{186} \item conditional expectation of $X$ given $\mathcal {G}$, - \hyperpage{341} - \item conditional expectation of $X$ given $Y$, \hyperpage{342} - \item conditional law of $X$ given $Y$, \hyperpage{342} + \hyperpage{345} + \item conditional expectation of $X$ given $Y$, \hyperpage{346} + \item conditional law of $X$ given $Y$, \hyperpage{346} \item conditional probability, \hyperpage{174} \item conditional probability density function, \hyperpage{182} \item conditional probability mass function, \hyperpage{182} @@ -505,7 +507,7 @@ \item configuration, \hyperpage{67} \item conformal, \hyperpage{119}, \hyperpage{149} \item conformal representation, \hyperpage{119} - \item conforming Galerkin method, \hyperpage{359} + \item conforming Galerkin method, \hyperpage{367} \item Congruence axioms, \hyperpage{63} \item congruence relation, \hyperpage{63} \item conic, \hyperpage{73} @@ -514,9 +516,9 @@ \item conjugate, \hyperpage{104}, \hyperpage{132}, \hyperpage{202}, \hyperpage{338} \item conjugate dynamical systems, \hyperpage{131} - \item Conjugate gradient, \hyperpage{348} + \item Conjugate gradient, \hyperpage{352} \item Conjugate gradient method, \hyperpage{264} - \item conjugate gradient method, \hyperpage{348} + \item conjugate gradient method, \hyperpage{352} \item conjugate Poisson kernel, \hyperpage{248} \item conjugation action, \hyperpage{41} \item connected, \hyperpage{50}, \hyperpage{54}, \hyperpage{214} @@ -538,20 +540,20 @@ \item Construction of a non-SAS geometry, \hyperpage{66} \item contact, \hyperpage{144} \item contact of order $\geq n$ at $a$, \hyperpage{31} - \item Continuation method, \hyperpage{352} + \item Continuation method, \hyperpage{359} \item Continuity axioms, \hyperpage{63} \item Continuity correction, \hyperpage{192} \item continuity correction, \hyperpage{192} \item Continuity from above, \hyperpage{173} \item Continuity from below, \hyperpage{173} \item continuous, \hyperpage{28}, \hyperpage{55}, \hyperpage{106}, - \hyperpage{130}, \hyperpage{313} + \hyperpage{130}, \hyperpage{354} \item continuous at $x_0$, \hyperpage{28} \item Continuous equation, \hyperpage{277} \item continuous equation, \hyperpage{277} - \item continuous Euler scheme, \hyperpage{357} + \item continuous Euler scheme, \hyperpage{363} \item Continuous function, \hyperpage{208} - \item continuous local martingale, \hyperpage{365} + \item continuous local martingale, \hyperpage{373} \item Continuous memorylessness property, \hyperpage{178} \item Continuous uniform distribution, \hyperpage{178} \item continuous uniform distribution, \hyperpage{178} @@ -559,8 +561,8 @@ \item contractible, \hyperpage{139} \item contraction, \hyperpage{55}, \hyperpage{90} \item contrast matrix, \hyperpage{201} - \item control parameter, \hyperpage{375} - \item control variate, \hyperpage{355} + \item control parameter, \hyperpage{383} + \item control variate, \hyperpage{361} \item converge in mean, \hyperpage{298} \item converge in norm $L^p$, \hyperpage{87} \item convergent, \hyperpage{26}, \hyperpage{54}, \hyperpage{76}, @@ -574,10 +576,10 @@ \item converges in probability, \hyperpage{187} \item converges in the $p$-th mean, \hyperpage{189} \item converges pointwise, \hyperpage{77, 78}, \hyperpage{106, 107} - \item converges strongly, \hyperpage{343} + \item converges strongly, \hyperpage{347} \item converges uniformly, \hyperpage{77, 78}, \hyperpage{106, 107} - \item converges weakly, \hyperpage{343} - \item converges weakly-*, \hyperpage{343} + \item converges weakly, \hyperpage{347} + \item converges weakly-*, \hyperpage{347} \item convex, \hyperpage{30}, \hyperpage{115} \item convex functional, \hyperpage{308} \item convolution, \hyperpage{79}, \hyperpage{240}, \hyperpage{244} @@ -627,7 +629,7 @@ \item cyclotomic, \hyperpage{170} \item càd, \hyperpage{326} \item càdlàg, \hyperpage{176} - \item Céa's lemma, \hyperpage{359} + \item Céa's lemma, \hyperpage{367} \indexspace @@ -653,8 +655,10 @@ \item Dehomogenization, \hyperpage{74} \item dehomogenization, \hyperpage{70} \item Delta method, \hyperpage{196} + \item Denjoy theorem, \hyperpage{343} + \item Denjoy-Koksma inequality, \hyperpage{342} \item dense, \hyperpage{207} - \item density, \hyperpage{278}, \hyperpage{341} + \item density, \hyperpage{278}, \hyperpage{345} \item density function, \hyperpage{178} \item Dependence on $\boldsymbol {\mathrm {\lambda }}$, \hyperpage{129} @@ -682,7 +686,7 @@ \item diagonal, \hyperpage{20} \item diagonalizable, \hyperpage{20} \item Diagonalization theorem, \hyperpage{20} - \item diameter, \hyperpage{360} + \item diameter, \hyperpage{368} \item dicyclic group, \hyperpage{42} \item diffeomorphism, \hyperpage{57} \item Differentiability criterion, \hyperpage{56} @@ -698,11 +702,11 @@ \item differential operator over distributions, \hyperpage{245} \item differential system, \hyperpage{122} \item differentiation operator, \hyperpage{285} - \item diffusion, \hyperpage{371} + \item diffusion, \hyperpage{379} \item diffusion coefficient, \hyperpage{278} \item Diffusion equation, \hyperpage{278} \item diffusion flux, \hyperpage{278} - \item diffusions, \hyperpage{372} + \item diffusions, \hyperpage{380} \item diffusivity, \hyperpage{278} \item digital topology, \hyperpage{206} \item dihedral group, \hyperpage{42} @@ -718,8 +722,8 @@ \item directional derivative, \hyperpage{55} \item director subspace, \hyperpage{70} \item Dirichlet, \hyperpage{274} - \item Dirichlet boundary condition, \hyperpage{350} - \item Dirichlet boundary conditions, \hyperpage{359} + \item Dirichlet boundary condition, \hyperpage{354} + \item Dirichlet boundary conditions, \hyperpage{367} \item Dirichlet kernel, \hyperpage{84}, \hyperpage{233} \item Dirichlet problem, \hyperpage{140}, \hyperpage{288} \item Dirichlet problem in the disc, \hyperpage{288} @@ -741,6 +745,7 @@ \item Discrete topology, \hyperpage{206} \item Discrete uniform distribution, \hyperpage{177} \item discrete uniform distribution, \hyperpage{177} + \item discretization method, \hyperpage{365} \item discriminant, \hyperpage{169} \item displacement current, \hyperpage{278} \item distance, \hyperpage{53}, \hyperpage{82}, \hyperpage{205}, @@ -755,7 +760,7 @@ \hyperpage{241} \item distributional derivative, \hyperpage{242}, \hyperpage{285} \item divergence, \hyperpage{61} - \item divergence form, \hyperpage{350} + \item divergence form, \hyperpage{354} \item Divergence theorem, \hyperpage{160} \item Divergence theorem on $\ensuremath {\mathbb {R}}^2$, \hyperpage{62} @@ -763,22 +768,22 @@ \hyperpage{62}, \hyperpage{160} \item divergent, \hyperpage{26}, \hyperpage{76}, \hyperpage{105, 106} \item divided difference, \hyperpage{93} - \item Doléans-Dade exponential, \hyperpage{370} + \item Doléans-Dade exponential, \hyperpage{378} \item domain, \hyperpage{115}, \hyperpage{148} \item dominant eigenvalue, \hyperpage{100} \item dominant eigenvector, \hyperpage{100} \item Dominated convergence theorem, \hyperpage{184}, \hyperpage{189}, - \hyperpage{297}, \hyperpage{340} - \item Doob's maximal inequality, \hyperpage{364} - \item Doob's optional sampling theorem, \hyperpage{364} + \hyperpage{297}, \hyperpage{344} + \item Doob's maximal inequality, \hyperpage{372} + \item Doob's optional sampling theorem, \hyperpage{372} \item Doob's optional sampling theorem for local martingales, - \hyperpage{365} + \hyperpage{373} \item dot product, \hyperpage{53} \item double, \hyperpage{90} \item Double dual space, \hyperpage{19} \item double dual space, \hyperpage{19} - \item drift, \hyperpage{371} - \item drift term, \hyperpage{369} + \item drift, \hyperpage{379} + \item drift term, \hyperpage{377} \item Du Bois-Reymond's test, \hyperpage{107} \item Du-Fort-Frankel scheme, \hyperpage{274} \item dual basis, \hyperpage{19} @@ -790,7 +795,7 @@ \item Duhamel principle, \hyperpage{287} \item dummy variable, \hyperpage{253} \item dyadic partition of order $n$, \hyperpage{183} - \item Dynamic programming principle, \hyperpage{374} + \item Dynamic programming principle, \hyperpage{382} \item dynamical system, \hyperpage{130} \indexspace @@ -811,7 +816,7 @@ \item elliptic equation, \hyperpage{277} \item elliptic point, \hyperpage{150} \item elliptic sector, \hyperpage{133} - \item embedded, \hyperpage{345} + \item embedded, \hyperpage{349} \item embedded methods, \hyperpage{260} \item empirical distribution, \hyperpage{202} \item empty set, \hyperpage{6} @@ -835,7 +840,7 @@ \item equivalence relation, \hyperpage{8} \item equivalent, \hyperpage{13}, \hyperpage{17}, \hyperpage{23}, \hyperpage{73}, \hyperpage{130}, \hyperpage{132}, - \hyperpage{306}, \hyperpage{356} + \hyperpage{306}, \hyperpage{362} \item equivalent dynamical systems, \hyperpage{131} \item Ergotic theorem, \hyperpage{324, 325} \item error of type I, \hyperpage{199} @@ -857,7 +862,7 @@ \item Euclidean vector space, \hyperpage{24} \item Euclidian division, \hyperpage{11} \item Euler characteristic, \hyperpage{218} - \item Euler method, \hyperpage{258}, \hyperpage{357} + \item Euler method, \hyperpage{258}, \hyperpage{363} \item Euler theorem, \hyperpage{50} \item Euler's formula, \hyperpage{108}, \hyperpage{150} \item Euler's theorem, \hyperpage{11} @@ -870,12 +875,12 @@ \item even extension, \hyperpage{84} \item even periodic extension, \hyperpage{283} \item event, \hyperpage{173} - \item events, \hyperpage{341} + \item events, \hyperpage{345} \item evolute, \hyperpage{144} \item exact, \hyperpage{156} \item Examples of Euclidean motions, \hyperpage{73} \item Excluded point topology, \hyperpage{206} - \item Existence and uniqueness of solutions of SDEs, \hyperpage{371} + \item Existence and uniqueness of solutions of SDEs, \hyperpage{379} \item Existence of a lift, \hyperpage{337} \item Existence of orthogonal polynomials, \hyperpage{96} \item Existence of the rotation number, \hyperpage{338} @@ -883,10 +888,10 @@ \item exists and it is finite, \hyperpage{298} \item expansion map, \hyperpage{335} \item Expansive fixed point theorem, \hyperpage{229} - \item Expectation, \hyperpage{183}, \hyperpage{341} + \item Expectation, \hyperpage{183}, \hyperpage{345} \item expectation, \hyperpage{178}, \hyperpage{182--184}, \hyperpage{249} - \item expectation of $X$, \hyperpage{341} + \item expectation of $X$, \hyperpage{345} \item explicit, \hyperpage{258} \item explicit Euler method, \hyperpage{258} \item explicit form, \hyperpage{122} @@ -901,8 +906,8 @@ \item exponential series, \hyperpage{48} \item extended complex plane, \hyperpage{105} \item extended real numbers, \hyperpage{105} - \item extension, \hyperpage{126}, \hyperpage{308}, \hyperpage{345} - \item extension operator, \hyperpage{345} + \item extension, \hyperpage{126}, \hyperpage{308}, \hyperpage{349} + \item extension operator, \hyperpage{349} \item exterior, \hyperpage{54} \item exterior angle, \hyperpage{160} \item Exterior angle theorem, \hyperpage{64} @@ -919,7 +924,7 @@ \item Fano configuration, \hyperpage{67} \item fast Fourier transform, \hyperpage{240} \item Fatou's lemma, \hyperpage{184}, \hyperpage{297}, - \hyperpage{340} + \hyperpage{344} \item feasible region, \hyperpage{51} \item feasible solution, \hyperpage{51} \item Fejér kernel, \hyperpage{85}, \hyperpage{234} @@ -929,7 +934,7 @@ \item FEM, \hyperpage{275} \item Fermat's little theorem, \hyperpage{11} \item Fermat's principle, \hyperpage{278} - \item Feynman-Kac's formula, \hyperpage{373} + \item Feynman-Kac's formula, \hyperpage{381} \item FFT, \hyperpage{240} \item Fick's law, \hyperpage{278} \item Fick's law of diffusion, \hyperpage{278} @@ -940,37 +945,38 @@ \item field of complex numbers, \hyperpage{104} \item field of fractions, \hyperpage{46}, \hyperpage{163} \item field of rational functions, \hyperpage{163} - \item filtered probability space, \hyperpage{342} - \item filtration, \hyperpage{321}, \hyperpage{342} + \item filtered probability space, \hyperpage{346} + \item filtration, \hyperpage{321}, \hyperpage{346} \item filtration space, \hyperpage{321} \item finer, \hyperpage{205} \item finer than, \hyperpage{32}, \hyperpage{58} \item finite, \hyperpage{25}, \hyperpage{49}, \hyperpage{164}, \hyperpage{213}, \hyperpage{294} \item finite $k$-th moment, \hyperpage{185} + \item finite difference estimator, \hyperpage{364} \item finite difference method, \hyperpage{265} \item finite difference scheme, \hyperpage{268} - \item finite element, \hyperpage{359} + \item finite element, \hyperpage{367} \item finite element method, \hyperpage{275} \item finite expectation, \hyperpage{182--184} \item Finite field, \hyperpage{166} \item finite field, \hyperpage{166} - \item Finite horizon problem, \hyperpage{375} + \item Finite horizon problem, \hyperpage{383} \item finite moment of order $k$, \hyperpage{185} \item Finite subadditivity, \hyperpage{173} - \item finite variation, \hyperpage{364} + \item finite variation, \hyperpage{372} \item Finite-dimensional distributions, \hyperpage{333} \item finite-dimensional distributions, \hyperpage{333} \item finite-rank operator, \hyperpage{307} \item finitely generated, \hyperpage{165} - \item firmly non-expansive, \hyperpage{347} + \item firmly non-expansive, \hyperpage{351} \item first and second characteristic polynomials, \hyperpage{261} \item First Borel-Cantelli lemma, \hyperpage{188} \item first fundamental form, \hyperpage{148} \item first integral, \hyperpage{134}, \hyperpage{154} \item First isomorphism theorem, \hyperpage{18}, \hyperpage{39}, \hyperpage{44} - \item first order reflection, \hyperpage{346} + \item first order reflection, \hyperpage{350} \item First Sylow theorem, \hyperpage{41} \item Fisher information, \hyperpage{195} \item Fisher's theorem, \hyperpage{197} @@ -986,10 +992,10 @@ \item flow, \hyperpage{128}, \hyperpage{132} \item Flow box theorem, \hyperpage{132} \item flow of the linear ODE, \hyperpage{126} - \item Flow property, \hyperpage{374} + \item Flow property, \hyperpage{382} \item flux, \hyperpage{62}, \hyperpage{159} - \item Fokker-Planck equation, \hyperpage{374} - \item formal adjoint, \hyperpage{350} + \item Fokker-Planck equation, \hyperpage{382} + \item formal adjoint, \hyperpage{356} \item Formal derivative, \hyperpage{167} \item formal derivative, \hyperpage{167} \item Forward and backward difference formula of order 1, @@ -1004,7 +1010,7 @@ \hyperpage{244}, \hyperpage{313} \item Fourier transform operator, \hyperpage{232} \item Fourier's law, \hyperpage{278} - \item Frank-Wolfe-type method, \hyperpage{347} + \item Frank-Wolfe-type method, \hyperpage{351} \item Fredholm alternative, \hyperpage{314} \item Fredholm operator with kernel $K$, \hyperpage{307} \item free variables, \hyperpage{14} @@ -1016,7 +1022,7 @@ \item FTBS, \hyperpage{268} \item FTCS, \hyperpage{268} \item FTFS, \hyperpage{268} - \item Fubini, \hyperpage{340} + \item Fubini, \hyperpage{344} \item Fubini's theorem, \hyperpage{59}, \hyperpage{175}, \hyperpage{300} \item Fubini's theorem for elementary regions, \hyperpage{59} @@ -1041,9 +1047,9 @@ \indexspace - \item Gagliardo, Nirengerg and Sobolev's inequality, \hyperpage{345} + \item Gagliardo, Nirengerg and Sobolev's inequality, \hyperpage{349} \item Galerkin approximation, \hyperpage{275} - \item Galerkin methods, \hyperpage{361} + \item Galerkin methods, \hyperpage{369} \item Galois, \hyperpage{168} \item Galois extension, \hyperpage{168} \item Galois group, \hyperpage{166} @@ -1080,42 +1086,42 @@ \item generalized eigenvector, \hyperpage{128} \item generalized heat kernel, \hyperpage{286} \item Generalized Hölder's inequality, \hyperpage{237} - \item generalized Itô integral, \hyperpage{368} + \item generalized Itô integral, \hyperpage{376} \item generalized solution, \hyperpage{245} \item generating set, \hyperpage{16} - \item Generator, \hyperpage{372} - \item generator, \hyperpage{372} + \item Generator, \hyperpage{380} + \item generator, \hyperpage{380} \item generator tree, \hyperpage{50} \item generatrix, \hyperpage{147} \item genus $g$ orientable surface, \hyperpage{217} \item genus $h$ non-orientable surface, \hyperpage{217} \item geodesic, \hyperpage{153} \item geodesic curvature, \hyperpage{153} - \item Geometric Brownian motion, \hyperpage{372} + \item Geometric Brownian motion, \hyperpage{380} \item Geometric distribution, \hyperpage{177} \item geometric distribution, \hyperpage{177} \item geometric multiplicity, \hyperpage{20} \item Gershgorin circle theorem, \hyperpage{92} - \item Giranov's theorem, \hyperpage{371} + \item Giranov's theorem, \hyperpage{379} \item Glide orthogonal reflections, \hyperpage{73} \item glide reflection, \hyperpage{72} \item glide vector, \hyperpage{73} \item Global Gau\ss -Bonnet theorem, \hyperpage{160} - \item global interpolant, \hyperpage{360} - \item Global interpolation error, \hyperpage{361} + \item global interpolant, \hyperpage{368} + \item Global interpolation error, \hyperpage{369} \item global maximum, \hyperpage{57} \item global minimum, \hyperpage{57} \item global stable manifold, \hyperpage{222} \item global truncation error, \hyperpage{258} \item global unstable manifold, \hyperpage{222} - \item globally smooth, \hyperpage{361} + \item globally smooth, \hyperpage{369} \item Goodness of fit, \hyperpage{200} \item Goursat's theorem, \hyperpage{112} \item Gra\ss mann formula, \hyperpage{16}, \hyperpage{67} \item gradient, \hyperpage{56} \item Gradient descent, \hyperpage{264} - \item Gradient descent algorithm, \hyperpage{347} - \item gradient descent algorithm, \hyperpage{347} + \item Gradient descent algorithm, \hyperpage{351} + \item gradient descent algorithm, \hyperpage{351} \item gradient vector field, \hyperpage{61} \item Gram-Schmidt process, \hyperpage{23}, \hyperpage{313} \item graph, \hyperpage{49}, \hyperpage{55}, \hyperpage{227} @@ -1127,7 +1133,7 @@ \item Green's formula, \hyperpage{159} \item Green's theorem, \hyperpage{62} \item grid, \hyperpage{268} - \item Gronwall's lemma, \hyperpage{371} + \item Gronwall's lemma, \hyperpage{379} \item Group, \hyperpage{37} \item group, \hyperpage{37} \item Group morphism, \hyperpage{38} @@ -1156,7 +1162,7 @@ \item heat flux, \hyperpage{278} \item heat kernel, \hyperpage{285} \item Heaviside step function, \hyperpage{242}, \hyperpage{285} - \item Heavy ball method, \hyperpage{348} + \item Heavy ball method, \hyperpage{352} \item Heine's theorem, \hyperpage{55} \item Heine-Borel theorem, \hyperpage{214} \item Hermite interpolation problem, \hyperpage{94} @@ -1177,7 +1183,7 @@ \item Hilbert-Schmidt operator with kernel $K$, \hyperpage{307} \item Hilbert-Schmidt spectral representation theorem, \hyperpage{314} - \item hitting time, \hyperpage{364} + \item hitting time, \hyperpage{372} \item holding times, \hyperpage{327} \item holes, \hyperpage{216} \item holomorphic, \hyperpage{109} @@ -1188,14 +1194,14 @@ \item homoclinic bifurcation, \hyperpage{226} \item homoclinic orbit, \hyperpage{133} \item homogeneous, \hyperpage{49}, \hyperpage{122}, \hyperpage{126}, - \hyperpage{350} - \item homogeneous adjoint problem, \hyperpage{350} + \hyperpage{354} + \item homogeneous adjoint problem, \hyperpage{356} \item homogeneous coordinates, \hyperpage{67} \item Homogeneous distribution, \hyperpage{245} \item homogeneous of degree $k$, \hyperpage{221} \item homogeneous of degree $r\in \ensuremath {\mathbb {R}}$, \hyperpage{245} - \item homogeneous SDE, \hyperpage{372} + \item homogeneous SDE, \hyperpage{380} \item Homogenization, \hyperpage{74} \item homogenization, \hyperpage{70} \item homography, \hyperpage{67} @@ -1205,7 +1211,7 @@ \item homotopic, \hyperpage{139} \item homotopy, \hyperpage{139} \item Hopf bifurcation theorem, \hyperpage{226} - \item Hopf's lemma, \hyperpage{352} + \item Hopf's lemma, \hyperpage{358} \item Hopf-bifurcation, \hyperpage{226} \item Hurwitz's theorem, \hyperpage{119} \item hyperbolic, \hyperpage{268}, \hyperpage{273} @@ -1226,7 +1232,7 @@ \item hypothesis test, \hyperpage{199} \item Hölder condition, \hyperpage{247} \item Hölder conjugates, \hyperpage{302} - \item Hölder continuity, \hyperpage{345} + \item Hölder continuity, \hyperpage{349} \item Hölder's inequality, \hyperpage{302, 303} \indexspace @@ -1243,12 +1249,12 @@ \item Immersion, \hyperpage{146} \item immersion, \hyperpage{146} \item implicit, \hyperpage{258} - \item implicit descent, \hyperpage{348} + \item implicit descent, \hyperpage{352} \item implicit Euler method, \hyperpage{258} \item implicit form, \hyperpage{122} \item Implicit function theorem, \hyperpage{57} \item Implicit scheme in finite differences, \hyperpage{286} - \item importance sampling estimator, \hyperpage{356} + \item importance sampling estimator, \hyperpage{362} \item improper, \hyperpage{37}, \hyperpage{203} \item improper integral, \hyperpage{79} \item in perspective with respect to a line, \hyperpage{68} @@ -1285,7 +1291,7 @@ \item infinite product topology, \hyperpage{209} \item infinitesimal generator, \hyperpage{328} \item infinitesimal transition scheme, \hyperpage{328} - \item Infinte horizon problem, \hyperpage{375} + \item Infinte horizon problem, \hyperpage{383} \item inflection point, \hyperpage{31} \item Information, \hyperpage{256} \item information of an event, \hyperpage{256} @@ -1297,8 +1303,8 @@ \item initial values, \hyperpage{48} \item injective, \hyperpage{7} \item inner product, \hyperpage{24}, \hyperpage{82}, \hyperpage{310} - \item Inner regularity, \hyperpage{351} - \item insphere diameter, \hyperpage{360} + \item Inner regularity, \hyperpage{357} + \item insphere diameter, \hyperpage{368} \item integrable, \hyperpage{32}, \hyperpage{182, 183} \item integrable function, \hyperpage{59} \item integrable function over $E$, \hyperpage{297} @@ -1314,7 +1320,7 @@ \item integral of $f$ over a measurable set $E\subseteq \ensuremath {\mathbb {R}}^n$, \hyperpage{296} \item integral of $f$ over the region $R$, \hyperpage{148} - \item integral of $f$ with respect to $\mu $, \hyperpage{340} + \item integral of $f$ with respect to $\mu $, \hyperpage{344} \item integral of $s$ over $\ensuremath {\mathbb {R}}^n$, \hyperpage{295} \item integral of $s$ over a measurable set $E$, \hyperpage{295} @@ -1326,14 +1332,14 @@ \item inter-arrival times, \hyperpage{327} \item Interior, \hyperpage{206} \item interior, \hyperpage{54}, \hyperpage{206} - \item interior ball condition, \hyperpage{352} + \item interior ball condition, \hyperpage{358} \item interior point, \hyperpage{54}, \hyperpage{157}, \hyperpage{207} \item interior product, \hyperpage{156} \item Intermediate value theorem, \hyperpage{28}, \hyperpage{55}, \hyperpage{94}, \hyperpage{215} \item internally studentized residuals, \hyperpage{254} - \item interpolant, \hyperpage{361, 362} + \item interpolant, \hyperpage{369, 370} \item Interpolation inequality, \hyperpage{303} \item interpolation problem, \hyperpage{93} \item intersection, \hyperpage{6} @@ -1342,8 +1348,8 @@ \item Intervals for $\mu $ and $\sigma ^2$, \hyperpage{198} \item invariance level, \hyperpage{71} \item Invariance of the MLE, \hyperpage{195} - \item Invariance under time shift, \hyperpage{372} - \item invariant, \hyperpage{131}, \hyperpage{339} + \item Invariance under time shift, \hyperpage{380} + \item invariant, \hyperpage{131}, \hyperpage{339, 340} \item invariant algebraic curve, \hyperpage{135} \item invariant subspace, \hyperpage{21} \item invariant under an affinity, \hyperpage{71} @@ -1373,7 +1379,7 @@ \item isolated singularity, \hyperpage{116}, \hyperpage{160} \item isometric, \hyperpage{23} \item isometry, \hyperpage{23}, \hyperpage{74}, \hyperpage{148}, - \hyperpage{366} + \hyperpage{374} \item isomorphic, \hyperpage{17}, \hyperpage{38}, \hyperpage{50}, \hyperpage{306} \item isomorphism, \hyperpage{38} @@ -1383,11 +1389,11 @@ \item iteration matrix, \hyperpage{99} \item itinerary, \hyperpage{230} \item Itinerary lemma, \hyperpage{229} - \item Itô integral, \hyperpage{368} - \item Itô isometry, \hyperpage{368} - \item Itô process, \hyperpage{369} - \item Itô term, \hyperpage{370} - \item Itô's formula, \hyperpage{370}, \hyperpage{374} + \item Itô integral, \hyperpage{376} + \item Itô isometry, \hyperpage{376} + \item Itô process, \hyperpage{377} + \item Itô term, \hyperpage{378} + \item Itô's formula, \hyperpage{378}, \hyperpage{382} \item ivp, \hyperpage{122} \indexspace @@ -1397,13 +1403,13 @@ \item Jacobian determinant, \hyperpage{55} \item Jacobian matrix, \hyperpage{55} \item Jeffrey's prior, \hyperpage{203} - \item Jensen's inequality, \hyperpage{236}, \hyperpage{341} + \item Jensen's inequality, \hyperpage{236}, \hyperpage{345} \item joint pdf, \hyperpage{180} \item joint pmf, \hyperpage{180} \item joint probability density function, \hyperpage{180} \item Joint probability mass function, \hyperpage{180} \item joint probability mass function, \hyperpage{180} - \item jointly Gaussian, \hyperpage{363} + \item jointly Gaussian, \hyperpage{371} \item Jordan arc, \hyperpage{61} \item Jordan block, \hyperpage{21} \item Jordan closed curve, \hyperpage{61} @@ -1425,10 +1431,10 @@ \item Kolmogorov system, \hyperpage{221} \item Kolmogorov's backward equation, \hyperpage{328} \item Kolmogorov's continuity theorem, \hyperpage{331} - \item Kolmogorov's equation, \hyperpage{372} + \item Kolmogorov's equation, \hyperpage{380} \item Kolmogorov's forward equation, \hyperpage{328} \item Kolmogorov's strong law of large numbers, \hyperpage{191} - \item Krasnoselskii-Mann's convergence theorem, \hyperpage{349} + \item Krasnoselskii-Mann's convergence theorem, \hyperpage{353} \item Kronecker delta, \hyperpage{19} \item Kronecker's lemma, \hyperpage{164} \item Kronecker's theorem, \hyperpage{167} @@ -1445,19 +1451,19 @@ \item Lagrange's theorem, \hyperpage{39} \item Laguerre polynomials, \hyperpage{96} \item Lamé coefficients, \hyperpage{277} - \item Langevin equation, \hyperpage{371} + \item Langevin equation, \hyperpage{379} \item Laplace equation, \hyperpage{140}, \hyperpage{288} \item Laplacian, \hyperpage{61} \item lattice of subgroups, \hyperpage{169} \item Laurent series, \hyperpage{117} \item Laurent series theorem, \hyperpage{117} - \item law of $X$, \hyperpage{341} + \item law of $X$, \hyperpage{345} \item Law of the iterated logarithm, \hyperpage{333} \item Law of total expectation, \hyperpage{186, 187}, \hyperpage{315} \item Law of total probability, \hyperpage{174}, \hyperpage{315} \item Lax theorem, \hyperpage{261} \item Lax-Friedrichs scheme, \hyperpage{268} - \item Lax-Milgram theorem, \hyperpage{313} + \item Lax-Milgram theorem, \hyperpage{355} \item Lax-Richtmyer equivalence theorem, \hyperpage{273} \item Lax-Wendroff, \hyperpage{271} \item Lax-Wendroff scheme, \hyperpage{271} @@ -1487,7 +1493,7 @@ \item level set, \hyperpage{55} \item leverage, \hyperpage{253} \item levorotation, \hyperpage{145} - \item Levy's characterization of Brownian motion, \hyperpage{366} + \item Levy's characterization of Brownian motion, \hyperpage{374} \item lexicographic degree, \hyperpage{163} \item lexicographic order, \hyperpage{163} \item lift, \hyperpage{337} @@ -1523,7 +1529,7 @@ \item linear programming to minimize, \hyperpage{51} \item linear recurrence relation of order $k$, \hyperpage{48} \item linear saddles, \hyperpage{227} - \item linear second-order PDE, \hyperpage{350} + \item linear second-order PDE, \hyperpage{354} \item linear span, \hyperpage{16} \item Linearity, \hyperpage{76} \item linearization, \hyperpage{221} @@ -1552,8 +1558,8 @@ \item local equivalence, \hyperpage{132} \item local extremum, \hyperpage{30}, \hyperpage{57} \item Local Gau\ss -Bonnet theorem, \hyperpage{160} - \item local interpolant, \hyperpage{360} - \item Local interpolation error, \hyperpage{361} + \item local interpolant, \hyperpage{368} + \item Local interpolation error, \hyperpage{369} \item local isometry, \hyperpage{148} \item local maximum, \hyperpage{30}, \hyperpage{57} \item local minimum, \hyperpage{30}, \hyperpage{57} @@ -1562,7 +1568,7 @@ \item local transversal section, \hyperpage{132} \item local truncation error, \hyperpage{262} \item local truncation errors, \hyperpage{258} - \item localizing sequence, \hyperpage{365} + \item localizing sequence, \hyperpage{373} \item locally, \hyperpage{214} \item locally bounded, \hyperpage{121}, \hyperpage{304} \item locally compact, \hyperpage{214} @@ -1580,6 +1586,7 @@ \item Logarithmic test, \hyperpage{76} \item logistic map, \hyperpage{228} \item logit, \hyperpage{257} + \item Longstaff-Schwartz method, \hyperpage{366} \item loop, \hyperpage{49}, \hyperpage{215} \item Lorenz system, \hyperpage{228} \item loss function, \hyperpage{203} @@ -1615,11 +1622,11 @@ \item marginal probability mass functions, \hyperpage{180} \item Markov chain, \hyperpage{318} \item Markov property, \hyperpage{318} - \item Markov property for Brownian motion, \hyperpage{363} + \item Markov property for Brownian motion, \hyperpage{371} \item Markov's inequality, \hyperpage{185} - \item Martingale, \hyperpage{363} - \item martingale, \hyperpage{342}, \hyperpage{363} - \item martingale term, \hyperpage{369} + \item Martingale, \hyperpage{371} + \item martingale, \hyperpage{346}, \hyperpage{371} + \item martingale term, \hyperpage{377} \item material derivative operator, \hyperpage{277} \item Matrix, \hyperpage{13} \item matrix, \hyperpage{13}, \hyperpage{18} @@ -1648,19 +1655,21 @@ \item Mean value theorem for vector-valued functions, \hyperpage{56} \item mean vector, \hyperpage{181}, \hyperpage{196} \item measurable, \hyperpage{175}, \hyperpage{293, 294}, - \hyperpage{340} - \item measurable space, \hyperpage{340} - \item Measure, \hyperpage{291}, \hyperpage{340} - \item measure, \hyperpage{174}, \hyperpage{291}, \hyperpage{340} + \hyperpage{344} + \item measurable space, \hyperpage{344} + \item Measure, \hyperpage{291}, \hyperpage{344} + \item measure, \hyperpage{174}, \hyperpage{291}, \hyperpage{344} + \item measure of $A$, \hyperpage{340} + \item measure of $U$, \hyperpage{340} \item measure on $\mathcal {C}(\ensuremath {\mathbb {T}}^1)$, - \hyperpage{338} - \item measure space, \hyperpage{175}, \hyperpage{340} + \hyperpage{339} + \item measure space, \hyperpage{175}, \hyperpage{344} \item Melnikov's method, \hyperpage{227} \item memoryless, \hyperpage{177, 178} \item meromorphic, \hyperpage{118} - \item Mersenne Twister algorithm, \hyperpage{354} + \item Mersenne Twister algorithm, \hyperpage{360} \item Mesh, \hyperpage{275} - \item mesh, \hyperpage{275}, \hyperpage{364} + \item mesh, \hyperpage{275}, \hyperpage{372} \item mesh-points, \hyperpage{258} \item Method of characteristics, \hyperpage{279} \item Method of moments, \hyperpage{194} @@ -1668,7 +1677,7 @@ \item metric space, \hyperpage{53}, \hyperpage{205}, \hyperpage{300} \item metrizable, \hyperpage{187}, \hyperpage{212} \item Meusnier's theorem, \hyperpage{150} - \item minimal, \hyperpage{221} + \item minimal, \hyperpage{221}, \hyperpage{340} \item minimal element, \hyperpage{9} \item minimal polynomial, \hyperpage{20} \item minimal surface, \hyperpage{149} @@ -1698,16 +1707,16 @@ \item moment-generating function, \hyperpage{186} \item monic, \hyperpage{11} \item Monotone convergence theorem, \hyperpage{184}, \hyperpage{296}, - \hyperpage{340} + \hyperpage{344} \item monotonic, \hyperpage{26}, \hyperpage{28} \item monotonically decreasing, \hyperpage{26} \item monotonically increasing, \hyperpage{26} - \item Montecarlo estimator, \hyperpage{354} + \item Montecarlo estimator, \hyperpage{360} \item Montel's theorem, \hyperpage{121} \item more efficient than, \hyperpage{194} \item Morera's theorem, \hyperpage{114} \item morphism of field extensions, \hyperpage{165} - \item Morrey's embedding, \hyperpage{345} + \item Morrey's embedding, \hyperpage{349} \item MSE, \hyperpage{194} \item multi-index notation, \hyperpage{57} \item multicollinearity, \hyperpage{255} @@ -1716,14 +1725,14 @@ \item Multinomial distrbution, \hyperpage{180} \item multinomial distribution, \hyperpage{180} \item multiple, \hyperpage{10} - \item multiple control variate estimator, \hyperpage{356} + \item multiple control variate estimator, \hyperpage{362} \item multiple edges, \hyperpage{49} \item Multiple shooting method, \hyperpage{264} \item multiple shooting method, \hyperpage{264} \item multiplicative group, \hyperpage{43} \item multiplicity, \hyperpage{114} \item multistep, \hyperpage{268} - \item multistep method, \hyperpage{348} + \item multistep method, \hyperpage{352} \item multivalued function, \hyperpage{104} \item multivariate cdf, \hyperpage{181} \item multivariate cumulative distribution function, \hyperpage{181} @@ -1741,33 +1750,36 @@ \indexspace + \item naive approach, \hyperpage{365} \item Nart-Vila theorem, \hyperpage{171} \item Natural cubic spline, \hyperpage{94} - \item natural filtration, \hyperpage{363} + \item natural filtration, \hyperpage{371} \item Navier-Cauchy equation, \hyperpage{277} \item negation, \hyperpage{8} \item negative, \hyperpage{141} \item negative basis, \hyperpage{142} \item Negative binomial distribution, \hyperpage{178} \item negative binomial distribution, \hyperpage{178} + \item negative orbit, \hyperpage{339} \item negative part, \hyperpage{77} \item negative semi-orbit, \hyperpage{130} \item negative-definite, \hyperpage{23} \item negative-semidefinite, \hyperpage{23} - \item negatively invariant, \hyperpage{131} + \item negatively invariant, \hyperpage{131}, \hyperpage{340} + \item negatively recurrent points, \hyperpage{340} \item negatively rotated, \hyperpage{227} \item negatively stable, \hyperpage{131} \item negatively-oriented, \hyperpage{142} \item neighbourhood, \hyperpage{25}, \hyperpage{54}, \hyperpage{207} - \item Nesterov's accelerated gradient method, \hyperpage{348} - \item Nesterov's method, \hyperpage{348} + \item Nesterov's accelerated gradient method, \hyperpage{352} + \item Nesterov's method, \hyperpage{352} \item Neumann, \hyperpage{274} - \item Neumann boundary condition, \hyperpage{350} - \item Neumann boundary conditions, \hyperpage{359} + \item Neumann boundary condition, \hyperpage{354} + \item Neumann boundary conditions, \hyperpage{367} \item Neumann series, \hyperpage{308} \item Neville's algorithm, \hyperpage{93} \item Newton method, \hyperpage{262}, \hyperpage{264}, - \hyperpage{348} + \hyperpage{352} \item Newton's divided differences\\method, \hyperpage{93} \item Newton-Raphson method, \hyperpage{90} \item Newton-Raphson modified method, \hyperpage{90} @@ -1786,13 +1798,14 @@ \item non-degenerate, \hyperpage{74} \item non-degenerated, \hyperpage{227} \item non-Desarguesian planes, \hyperpage{68} - \item non-divergence form, \hyperpage{350} + \item non-divergence form, \hyperpage{354} \item Non-parametric bootstrap, \hyperpage{202} \item Non-Paschian geometry, \hyperpage{65} \item Non-SAS geometry, \hyperpage{66} \item non-singular, \hyperpage{131} + \item non-wandering, \hyperpage{340} \item noncommutative ring, \hyperpage{42} - \item nonexpansive, \hyperpage{348} + \item nonexpansive, \hyperpage{352} \item nonsingular, \hyperpage{22} \item norm, \hyperpage{24}, \hyperpage{53}, \hyperpage{94}, \hyperpage{300}, \hyperpage{305} @@ -1817,7 +1830,7 @@ \item normed vector space, \hyperpage{53}, \hyperpage{300} \item not integrable, \hyperpage{182} \item not orientation-preserving, \hyperpage{217} - \item Novikov's condition, \hyperpage{370} + \item Novikov's condition, \hyperpage{378} \item null hypothesis, \hyperpage{199} \item null recurrent, \hyperpage{324} \item null set, \hyperpage{174}, \hyperpage{293} @@ -1853,9 +1866,10 @@ \item Open mapping theorem, \hyperpage{116}, \hyperpage{309} \item open sets, \hyperpage{205} \item operator, \hyperpage{124}, \hyperpage{305} - \item Opial's lemma, \hyperpage{348} + \item Opial's lemma, \hyperpage{352} \item opposite orientations, \hyperpage{142}, \hyperpage{217} - \item orbit, \hyperpage{8}, \hyperpage{40}, \hyperpage{130} + \item orbit, \hyperpage{8}, \hyperpage{40}, \hyperpage{130}, + \hyperpage{339} \item Orbit linear structure, \hyperpage{8} \item Orbit structure, \hyperpage{8} \item Orbit-stabilizer theorem, \hyperpage{40} @@ -1896,7 +1910,7 @@ \item orthogonal system, \hyperpage{313} \item orthogonal with respect to the weight $\omega (x)$, \hyperpage{96} - \item Orthogonality of martingales, \hyperpage{364} + \item Orthogonality of martingales, \hyperpage{372} \item orthonormal, \hyperpage{22}, \hyperpage{82} \item orthonormal system, \hyperpage{82}, \hyperpage{313} \item orthonormalization, \hyperpage{313} @@ -1935,7 +1949,7 @@ \item partial differential equation, \hyperpage{139} \item Partial fraction decomposition theorem, \hyperpage{117} \item partial inverse Fourier transform, \hyperpage{233} - \item partial isometry, \hyperpage{366} + \item partial isometry, \hyperpage{374} \item partial order relation, \hyperpage{9} \item Partial pivoting, \hyperpage{102} \item partially ordered set, \hyperpage{9} @@ -1996,12 +2010,12 @@ \item Poincaré index formula, \hyperpage{139} \item Poincaré inequality, \hyperpage{289} \item Poincaré map, \hyperpage{136} - \item Poincaré's inequality, \hyperpage{344} + \item Poincaré's inequality, \hyperpage{348} \item Poincaré's method, \hyperpage{226} \item Poincaré-Bendixson theorem, \hyperpage{136} \item Poincaré-Hopf theorem, \hyperpage{139}, \hyperpage{161} \item Poincaré-Hopf theorem on $S^2$, \hyperpage{139} - \item Poincaré-Wirtinger's inequality, \hyperpage{344} + \item Poincaré-Wirtinger's inequality, \hyperpage{348} \item points, \hyperpage{63}, \hyperpage{205} \item points of the quadric, \hyperpage{73} \item pointwise bounded, \hyperpage{125}, \hyperpage{304} @@ -2013,7 +2027,7 @@ \item Poisson summation formula, \hyperpage{238}, \hyperpage{240} \item Polar form, \hyperpage{108} \item polar form, \hyperpage{108} - \item Polar method, \hyperpage{355} + \item Polar method, \hyperpage{361} \item Polarization identity, \hyperpage{310} \item Pole, \hyperpage{116} \item pole, \hyperpage{116} @@ -2032,13 +2046,15 @@ \item poset, \hyperpage{9} \item positive, \hyperpage{141}, \hyperpage{158} \item positive basis, \hyperpage{142} + \item positive orbit, \hyperpage{339} \item positive part, \hyperpage{77} \item positive recurrent, \hyperpage{324} \item positive semi-orbit, \hyperpage{130} \item positive-definite, \hyperpage{23} \item positive-semidefinite, \hyperpage{23} - \item positively invariant, \hyperpage{131} + \item positively invariant, \hyperpage{131}, \hyperpage{340} \item positively oriented, \hyperpage{142} + \item positively recurrent points, \hyperpage{340} \item positively rotated, \hyperpage{227} \item positively stable, \hyperpage{131} \item posterior, \hyperpage{202} @@ -2060,6 +2076,7 @@ \item preditions, \hyperpage{250} \item preimage, \hyperpage{7} \item preserves orientation, \hyperpage{337} + \item price of an American option, \hyperpage{365} \item primal, \hyperpage{51} \item prime, \hyperpage{10}, \hyperpage{12}, \hyperpage{44} \item Prime number theorem, \hyperpage{10} @@ -2080,18 +2097,18 @@ \item prior distribution, \hyperpage{202} \item probability, \hyperpage{173} \item probability density function, \hyperpage{178} - \item probability kernel, \hyperpage{342} + \item probability kernel, \hyperpage{346} \item Probability mass function, \hyperpage{176} \item probability mass function, \hyperpage{176} - \item probability measure, \hyperpage{338} - \item probability space, \hyperpage{173}, \hyperpage{341} + \item probability measure, \hyperpage{339} + \item probability space, \hyperpage{173}, \hyperpage{345} \item probability-generating function, \hyperpage{316} \item product, \hyperpage{11}, \hyperpage{13}, \hyperpage{106} - \item Product measure, \hyperpage{340} - \item product measure, \hyperpage{340} + \item Product measure, \hyperpage{344} + \item product measure, \hyperpage{344} \item product topology, \hyperpage{209} \item products of group subsets, \hyperpage{40} - \item progressive, \hyperpage{367} + \item progressive, \hyperpage{375} \item projection, \hyperpage{71} \item Projection theorem, \hyperpage{311} \item Projections, \hyperpage{71} @@ -2118,7 +2135,7 @@ \item pure death process, \hyperpage{329} \item purely inseparable, \hyperpage{168} \item purely transcendental, \hyperpage{165} - \item pushforward measure, \hyperpage{339} + \item push-forward measure, \hyperpage{339} \item Pythagorean, \hyperpage{64} \item Pythagorean plane, \hyperpage{64} \item Pythagorean theorem, \hyperpage{72}, \hyperpage{310} @@ -2133,8 +2150,8 @@ \item Quadratic loss function, \hyperpage{203} \item quadratic polynomial, \hyperpage{162} \item quadratic space, \hyperpage{74} - \item Quadratic variation, \hyperpage{364} - \item quadratic variation, \hyperpage{369} + \item Quadratic variation, \hyperpage{372} + \item quadratic variation, \hyperpage{377} \item quadrature formula, \hyperpage{95} \item quadrature formula with weight $\omega (x)$, \hyperpage{97} \item quadric, \hyperpage{73} @@ -2162,10 +2179,10 @@ \item radius of curvature, \hyperpage{144} \item radix-2 decimation-in-time (DIT) FFT, \hyperpage{240} \item Radix-2 DIT Cooley-Tukey FFT algorithm, \hyperpage{240} - \item Radon-Nikodym, \hyperpage{341} + \item Radon-Nikodym, \hyperpage{345} \item Radó theorem, \hyperpage{218} \item random sample, \hyperpage{193} - \item Random variable, \hyperpage{341} + \item Random variable, \hyperpage{345} \item random variable, \hyperpage{175} \item random vector, \hyperpage{179} \item Random walk, \hyperpage{319} @@ -2209,13 +2226,13 @@ \item Regula falsi method, \hyperpage{90} \item regular, \hyperpage{49}, \hyperpage{58}, \hyperpage{131}, \hyperpage{141}, \hyperpage{195, 196}, \hyperpage{212}, - \hyperpage{328}, \hyperpage{361} + \hyperpage{328}, \hyperpage{369} \item regular distributions, \hyperpage{241} \item regular domain, \hyperpage{148} \item regular region, \hyperpage{160} \item regular surface, \hyperpage{147} - \item Regularity up to the boundary, \hyperpage{351} - \item Reillich-Kondrachov's compactness theorem, \hyperpage{346} + \item Regularity up to the boundary, \hyperpage{357} + \item Reillich-Kondrachov's compactness theorem, \hyperpage{350} \item Related samples with unknown variances, \hyperpage{199} \item relative condition numbers, \hyperpage{90} \item relative error, \hyperpage{89} @@ -2233,7 +2250,7 @@ \item residuals, \hyperpage{250} \item residue, \hyperpage{116} \item Residues theorem, \hyperpage{117} - \item resolvent set, \hyperpage{351} + \item resolvent set, \hyperpage{356} \item response, \hyperpage{253} \item restrictions, \hyperpage{51} \item Reuter criterion, \hyperpage{330} @@ -2261,11 +2278,13 @@ \item ring, \hyperpage{42} \item Ring morphism, \hyperpage{43} \item ring morphism, \hyperpage{43} + \item risk-free interest rate, \hyperpage{365} \item RK methods, \hyperpage{260} \item Robin, \hyperpage{274} - \item Robin boundary conditions, \hyperpage{359} + \item Robin boundary conditions, \hyperpage{367} + \item Rogers's lemma, \hyperpage{366} \item Rolle's theorem, \hyperpage{30} - \item Romberg Extrapolation, \hyperpage{357} + \item Romberg Extrapolation, \hyperpage{363} \item Romberg method, \hyperpage{96} \item root, \hyperpage{12} \item root condition, \hyperpage{262} @@ -2281,9 +2300,9 @@ \item row rank, \hyperpage{16} \item Ruffini's rule, \hyperpage{12} \item ruled surface, \hyperpage{151} - \item Runge phenomenon, \hyperpage{362} + \item Runge's phenomenon, \hyperpage{94} \item Runge-Kutta-Fehlberg method, \hyperpage{260} - \item running cost, \hyperpage{375} + \item running cost, \hyperpage{383} \indexspace @@ -2306,8 +2325,8 @@ \item SAS criterion, \hyperpage{63, 64} \item scalars, \hyperpage{15} \item scale, \hyperpage{179} - \item Schaefer fixed point, \hyperpage{353} - \item Schauder fixed point, \hyperpage{353} + \item Schaefer fixed point, \hyperpage{359} + \item Schauder fixed point, \hyperpage{359} \item Schrödinger equation, \hyperpage{279} \item Schwartz space, \hyperpage{243} \item Schwarz lemma, \hyperpage{120} @@ -2317,7 +2336,7 @@ \item score function, \hyperpage{195} \item Score test, \hyperpage{202} \item score test, \hyperpage{202} - \item SDE, \hyperpage{371} + \item SDE, \hyperpage{379} \item Secant method, \hyperpage{90} \item secant-like method, \hyperpage{263} \item Second Borel-Cantelli lemma, \hyperpage{189} @@ -2328,7 +2347,7 @@ \item Second Sylow theorem, \hyperpage{41} \item section, \hyperpage{299} \item sectorial decomposition, \hyperpage{133} - \item seed, \hyperpage{354} + \item seed, \hyperpage{360} \item segment, \hyperpage{72} \item Segmented regression, \hyperpage{253} \item self-adjoint, \hyperpage{312} @@ -2415,11 +2434,11 @@ \item Slutsky's theorem, \hyperpage{190} \item small change, \hyperpage{279} \item Sobolev space, \hyperpage{289} - \item Sobolev spaces, \hyperpage{344} + \item Sobolev spaces, \hyperpage{348} \item solution, \hyperpage{90}, \hyperpage{139} \item solution of a system of equations, \hyperpage{13} \item solution of the ODE, \hyperpage{122} - \item solution of the SDE, \hyperpage{371} + \item solution of the SDE, \hyperpage{379} \item solvable, \hyperpage{41}, \hyperpage{170} \item solvable by radicals, \hyperpage{170} \item SOR, \hyperpage{100} @@ -2427,11 +2446,11 @@ \item space of rapidly decreasing functions, \hyperpage{243} \item special orthogonal group, \hyperpage{145} \item specific heat capacity, \hyperpage{278} - \item spectral methods, \hyperpage{361} + \item spectral methods, \hyperpage{369} \item spectral radius, \hyperpage{98} - \item Spectral theorem, \hyperpage{24}, \hyperpage{314} + \item Spectral theorem, \hyperpage{24}, \hyperpage{313} \item spectral values, \hyperpage{309} - \item spectrum, \hyperpage{97}, \hyperpage{309}, \hyperpage{351} + \item spectrum, \hyperpage{97}, \hyperpage{309}, \hyperpage{356} \item sphere, \hyperpage{54} \item Spline, \hyperpage{94} \item spline, \hyperpage{94} @@ -2478,10 +2497,10 @@ \item stiff equations, \hyperpage{261} \item stiffness matrix, \hyperpage{276} \item Stirling's formula, \hyperpage{81} - \item stochastic differential, \hyperpage{369} - \item stochastic differential equation, \hyperpage{371} - \item Stochastic dominated convergence theorem, \hyperpage{368} - \item Stochastic integration by parts, \hyperpage{370} + \item stochastic differential, \hyperpage{377} + \item stochastic differential equation, \hyperpage{379} + \item Stochastic dominated convergence theorem, \hyperpage{376} + \item Stochastic integration by parts, \hyperpage{378} \item Stochastic matrix, \hyperpage{318} \item stochastic matrix, \hyperpage{318} \item Stochastic process, \hyperpage{316} @@ -2491,8 +2510,8 @@ \item Stokes' theorem, \hyperpage{62} \item Stolz-Cesàro theorem, \hyperpage{27} \item Stone-Weierstra\ss \ theorem, \hyperpage{304} - \item stopped process, \hyperpage{342}, \hyperpage{364} - \item stopping time, \hyperpage{321}, \hyperpage{342} + \item stopped process, \hyperpage{346}, \hyperpage{372} + \item stopping time, \hyperpage{321}, \hyperpage{346} \item strict Lyapunov function, \hyperpage{137} \item strictly concave, \hyperpage{30} \item strictly convex, \hyperpage{30} @@ -2501,16 +2520,16 @@ \item strictly diagonally dominant by rows, \hyperpage{99} \item strictly increasing, \hyperpage{26}, \hyperpage{28} \item Strong duality theorem, \hyperpage{52} - \item Strong error of the Euler scheme, \hyperpage{357} + \item Strong error of the Euler scheme, \hyperpage{363} \item Strong law of large numbers, \hyperpage{191} \item Strong law of large numbers for Brownian motion, - \hyperpage{363} + \hyperpage{371} \item Strong Markov property, \hyperpage{321, 322} - \item Strong maximum principle, \hyperpage{352} - \item strong solution, \hyperpage{352} + \item Strong maximum principle, \hyperpage{358} + \item strong solution, \hyperpage{354} \item strongly consistent estimator, \hyperpage{194} - \item strongly convex, \hyperpage{347} - \item strongly lower-semicontinuous, \hyperpage{343} + \item strongly convex, \hyperpage{351} + \item strongly lower-semicontinuous, \hyperpage{347} \item Structal stability, \hyperpage{336} \item Strum's sequence, \hyperpage{92} \item Student's $t$-distribution with $n$ degrees of freedom, @@ -2518,22 +2537,22 @@ \item Sturm's sequence, \hyperpage{92} \item Sturm's theorem, \hyperpage{92} \item Sturm-Picone comparison theorem, \hyperpage{283} - \item sub-martingale, \hyperpage{363} + \item sub-martingale, \hyperpage{371} \item sub-multiplicativity, \hyperpage{97} \item subadditive, \hyperpage{338} \item subalgebra, \hyperpage{303} \item subbasis, \hyperpage{206} \item subcover, \hyperpage{213} - \item subdivision, \hyperpage{360} + \item subdivision, \hyperpage{368} \item subfield generated, \hyperpage{163} - \item subgradient descent method, \hyperpage{348} + \item subgradient descent method, \hyperpage{352} \item Subgroup, \hyperpage{37} \item subgroup, \hyperpage{37} \item subgroup generated, \hyperpage{37} \item sublinear, \hyperpage{306} \item submanifold, \hyperpage{146} \item submanifold with boundary, \hyperpage{157} - \item submartingale, \hyperpage{342} + \item submartingale, \hyperpage{346} \item Submersion, \hyperpage{146} \item submersion, \hyperpage{146} \item subordinated matrix norm, \hyperpage{97} @@ -2556,12 +2575,13 @@ \hyperpage{107} \item sum of the series in an uniform sense, \hyperpage{78}, \hyperpage{107} - \item super-martingale, \hyperpage{363} + \item super-martingale, \hyperpage{371} \item superadditive, \hyperpage{338} - \item supermartingale, \hyperpage{342} + \item supermartingale, \hyperpage{346} \item support, \hyperpage{8}, \hyperpage{79}, \hyperpage{146}, \hyperpage{176}, \hyperpage{180}, \hyperpage{242} - \item support plane, \hyperpage{343} + \item support of $\mu $, \hyperpage{340} + \item support plane, \hyperpage{347} \item support points, \hyperpage{93} \item supremum, \hyperpage{25} \item Supremum axiom, \hyperpage{25} @@ -2576,7 +2596,7 @@ \item Sylow $p$-subgroup, \hyperpage{41} \item Sylvester's criterion, \hyperpage{58} \item Sylvester's law of inertia, \hyperpage{23} - \item symmetric, \hyperpage{22}, \hyperpage{62}, \hyperpage{313} + \item symmetric, \hyperpage{22}, \hyperpage{62}, \hyperpage{354} \item Symmetric difference formula of order 1, \hyperpage{95} \item Symmetric difference formula of order 2, \hyperpage{95} \item symmetric group, \hyperpage{8}, \hyperpage{38} @@ -2597,6 +2617,7 @@ \item tangent line to the graph at the point $(x_0,f(x_0))$, \hyperpage{29} \item tangent plane, \hyperpage{147} + \item tangent process, \hyperpage{364} \item tangent space, \hyperpage{147}, \hyperpage{156, 157} \item tangent vector, \hyperpage{141}, \hyperpage{147}, \hyperpage{156} @@ -2609,7 +2630,7 @@ \item Taylor's theorem, \hyperpage{57} \item tempered distribution, \hyperpage{244} \item tends to the boundary, \hyperpage{126} - \item terminal cost, \hyperpage{375} + \item terminal cost, \hyperpage{383} \item terminal point, \hyperpage{215} \item test, \hyperpage{200} \item test functions, \hyperpage{240} @@ -2658,9 +2679,9 @@ \item totally isotropic, \hyperpage{74} \item Tower formula, \hyperpage{165} \item tower of fields, \hyperpage{165} - \item Tower property, \hyperpage{342} + \item Tower property, \hyperpage{346} \item trace, \hyperpage{141}, \hyperpage{289} - \item trace operator, \hyperpage{346} + \item trace operator, \hyperpage{350} \item Trace theorem, \hyperpage{289} \item Traffic flow equation, \hyperpage{280} \item trail, \hyperpage{49} @@ -2683,14 +2704,14 @@ \item Trapezoidal rule, \hyperpage{95} \item traversable, \hyperpage{50} \item tree, \hyperpage{50} - \item trial functions, \hyperpage{361} + \item trial functions, \hyperpage{369} \item triangle, \hyperpage{160} \item Triangular inequality, \hyperpage{25}, \hyperpage{72} \item triangular inequality, \hyperpage{53}, \hyperpage{205}, \hyperpage{300} \item triangular system, \hyperpage{97} \item triangularization, \hyperpage{218} - \item triangulation, \hyperpage{360} + \item triangulation, \hyperpage{368} \item triple, \hyperpage{90} \item trivial $\sigma $-algebra, \hyperpage{172} \item Trivial topology, \hyperpage{206} @@ -2698,6 +2719,7 @@ \item truncated, \hyperpage{266} \item truncated Hilbert transform, \hyperpage{247} \item truncated singular value decomposition, \hyperpage{266} + \item Tsitsiklis-Van Roy method, \hyperpage{365} \item TSVD, \hyperpage{266} \item two times differentiable, \hyperpage{31} \item two times differentiable at $a$, \hyperpage{31} @@ -2722,12 +2744,13 @@ \item uniformly bounded, \hyperpage{125}, \hyperpage{304} \item uniformly continuous, \hyperpage{33}, \hyperpage{55} \item uniformly convergent, \hyperpage{117} - \item uniformly elliptic, \hyperpage{350} + \item uniformly elliptic, \hyperpage{354} \item uniformly equicontinuous, \hyperpage{125}, \hyperpage{304} - \item uniformly integrable, \hyperpage{342} + \item uniformly integrable, \hyperpage{346} \item uniformly most powerful, \hyperpage{200} \item union, \hyperpage{6} \item unique factorization domain, \hyperpage{45} + \item uniquely ergodic, \hyperpage{341} \item Uniqueness of Dirichlet problem, \hyperpage{288} \item Uniqueness of the heat equation, \hyperpage{287} \item Uniqueness of the heat equation on the unbounded domains, @@ -2768,7 +2791,7 @@ \item variance inflation factor, \hyperpage{255} \item Variation of constants, \hyperpage{123} \item variational equations, \hyperpage{129} - \item variational formulation, \hyperpage{275} + \item variational formulation, \hyperpage{275}, \hyperpage{354} \item Variations without repetition, \hyperpage{10} \item vector field, \hyperpage{60}, \hyperpage{152}, \hyperpage{154}, \hyperpage{156} @@ -2791,18 +2814,21 @@ \item Wald test, \hyperpage{201} \item Wald theorem, \hyperpage{315} \item walk, \hyperpage{49} + \item wandering domain, \hyperpage{340} + \item wandering point, \hyperpage{340} \item Waring's method, \hyperpage{164} \item Wave equation, \hyperpage{140}, \hyperpage{277} \item wave equation, \hyperpage{140} \item wave function, \hyperpage{279} \item Weak duality theorem, \hyperpage{51} - \item Weak error of the Euler scheme, \hyperpage{357} - \item weak formulation, \hyperpage{275}, \hyperpage{350} + \item Weak error of the Euler scheme, \hyperpage{363} + \item weak formulation, \hyperpage{275}, \hyperpage{354} \item Weak law of large numbers, \hyperpage{190} - \item Weak maximum principle, \hyperpage{351, 352} - \item weak-* lower-semicontinuity, \hyperpage{343} + \item Weak maximum principle, \hyperpage{357, 358} + \item weak solution, \hyperpage{354} + \item weak-* lower-semicontinuity, \hyperpage{347} \item weakly consistent estimator, \hyperpage{194} - \item weakly lower-semicontinuity, \hyperpage{343} + \item weakly lower-semicontinuity, \hyperpage{347} \item Weierstra\ss ' theorem, \hyperpage{55}, \hyperpage{114}, \hyperpage{214} \item Weierstra\ss \ approximation theorem, \hyperpage{79} @@ -2815,8 +2841,8 @@ \item well-ordered set, \hyperpage{9} \item well-posed, \hyperpage{258} \item well-posed in the Hadamard sense, \hyperpage{258} - \item Wiener integral, \hyperpage{366} - \item Wiener isometry, \hyperpage{366} + \item Wiener integral, \hyperpage{374} + \item Wiener isometry, \hyperpage{374} \item Wiener process, \hyperpage{330} \item winding number, \hyperpage{113} \item Wintner lemma, \hyperpage{126} diff --git a/main_math.tex b/main_math.tex index 99f1fe4..e2f76bf 100644 --- a/main_math.tex +++ b/main_math.tex @@ -1,5 +1,6 @@ \documentclass[10pt,a4paper]{report} -\usepackage{preamble_formulas} +\usepackage{preamble_general} +\usepackage{preamble_math} \usepackage{preamble_style} \title{Summaries of the Mathematics degree at UAB} diff --git a/main_physics.idx b/main_physics.idx index 1d79a89..eae497b 100644 --- a/main_physics.idx +++ b/main_physics.idx @@ -497,7 +497,16 @@ \indexentry{kinematic viscosity|hyperpage}{44} \indexentry{characteristic length|hyperpage}{44} \indexentry{characteristic velocity|hyperpage}{44} +\indexentry{convective term|hyperpage}{44} +\indexentry{inertia term|hyperpage}{44} +\indexentry{diffusive term|hyperpage}{44} +\indexentry{dissipation term|hyperpage}{44} \indexentry{characteristic length|hyperpage}{44} \indexentry{characteristic velocity|hyperpage}{44} \indexentry{Reynolds number|hyperpage}{44} \indexentry{similar|hyperpage}{44} +\indexentry{Helmholtz-Hodge decomposition theorem|hyperpage}{44} +\indexentry{Stokes' equations|hyperpage}{45} +\indexentry{equation of state|hyperpage}{45} +\indexentry{speed of sound|hyperpage}{45} +\indexentry{Mach number|hyperpage}{45} diff --git a/main_physics.ilg b/main_physics.ilg index 9e4190e..54ae92e 100644 --- a/main_physics.ilg +++ b/main_physics.ilg @@ -1,6 +1,6 @@ This is makeindex, version 2.17 [TeX Live 2023] (kpathsea + Thai support). -Scanning input file main_physics.idx....done (503 entries accepted, 0 rejected). -Sorting entries.......done (4815 comparisons). -Generating output file main_physics.ind....done (555 lines written, 0 warnings). +Scanning input file main_physics.idx....done (512 entries accepted, 0 rejected). +Sorting entries.......done (4973 comparisons). +Generating output file main_physics.ind....done (564 lines written, 0 warnings). Output written in main_physics.ind. Transcript written in main_physics.ilg. diff --git a/main_physics.ind b/main_physics.ind index aa4848d..73e368d 100644 --- a/main_physics.ind +++ b/main_physics.ind @@ -108,6 +108,7 @@ \item control roads, \hyperpage{26} \item Convection, \hyperpage{29} \item convection, \hyperpage{29} + \item convective term, \hyperpage{44} \item Coulomb's law, \hyperpage{4} \item crystalline, \hyperpage{28} \item Curvature, \hyperpage{11} @@ -124,10 +125,12 @@ \item Density, \hyperpage{16} \item diamagnetic, \hyperpage{9} \item Diffusion equation, \hyperpage{29} + \item diffusive term, \hyperpage{44} \item discharge of a fluid, \hyperpage{17} \item displacement current, \hyperpage{10} \item Dissipated power, \hyperpage{17} \item dissipated power, \hyperpage{17} + \item dissipation term, \hyperpage{44} \item Distribution of molecular velocities, \hyperpage{19} \item down, \hyperpage{27} \item Drag forces, \hyperpage{18} @@ -161,6 +164,7 @@ \item Entropy, \hyperpage{33} \item entropy, \hyperpage{33} \item equation of movement, \hyperpage{11} + \item equation of state, \hyperpage{45} \item Equipartition theorem, \hyperpage{20} \item Equipartition theorem on diatomic molecules, \hyperpage{20} \item Examples of potential energies, \hyperpage{14} @@ -224,6 +228,7 @@ \item Heisenberg's uncertainty principle, \hyperpage{21} \item Helmholtz free energy, \hyperpage{33} \item Helmholtz's theorem, \hyperpage{43} + \item Helmholtz-Hodge decomposition theorem, \hyperpage{44} \item Hermitian, \hyperpage{36} \item Hilbert space, \hyperpage{35} \item homogeneous, \hyperpage{40} @@ -236,6 +241,7 @@ \item ideal fluid, \hyperpage{39} \item incompressible, \hyperpage{16}, \hyperpage{40} \item inductor, \hyperpage{10} + \item inertia term, \hyperpage{44} \item inertial force, \hyperpage{12} \item Inertial forces, \hyperpage{12} \item inertial frame of reference, \hyperpage{14} @@ -298,6 +304,7 @@ \indexspace + \item Mach number, \hyperpage{45} \item Macroscopic Ohm's law, \hyperpage{6} \item magnetic flux, \hyperpage{9} \item magnetic moment, \hyperpage{7} @@ -453,6 +460,7 @@ \item spectral decomposition, \hyperpage{36} \item spectral radiance, \hyperpage{20} \item speed, \hyperpage{11} + \item speed of sound, \hyperpage{45} \item Spin, \hyperpage{23} \item spin, \hyperpage{23} \item spin quantum number, \hyperpage{23} @@ -466,6 +474,7 @@ \item steady, \hyperpage{41} \item Stefan-Boltzmann law, \hyperpage{20} \item Stern-Gerlach, \hyperpage{37} + \item Stokes' equations, \hyperpage{45} \item Stopping potential, \hyperpage{21} \item strange, \hyperpage{27} \item stream function, \hyperpage{43} diff --git a/main_physics.tex b/main_physics.tex index ad37dd3..77b63aa 100644 --- a/main_physics.tex +++ b/main_physics.tex @@ -1,6 +1,7 @@ \documentclass[10pt,a4paper]{report} -\usepackage{preamble_formulas} +\usepackage{preamble_general} \usepackage{preamble_style} +\usepackage{preamble_math} \title{Summaries of Physics degree at UAB} \author{Víctor Ballester} diff --git a/preamble_general.sty b/preamble_general.sty new file mode 100644 index 0000000..da9d291 --- /dev/null +++ b/preamble_general.sty @@ -0,0 +1,253 @@ +\usepackage{amsthm, amsmath, mathtools, amssymb, physics} % for math and physics commands and symbols. +\usepackage[intlimits]{esint} % for more options on integrals. +\usepackage{standalone} % for compiling individually .tex images. +\usepackage[hypcap=false]{caption} % basically for using the command \captionof{}, which is useful in some environments, others than \begin{figure}. +\usepackage{subcaption} % for subfigures, when many captions come into play. +\usepackage{multicol} % organize the whole document in multiple columns. +\usepackage[USenglish]{babel} % for improving use of English and mainly the use of hyphenation. +\usepackage[version=4]{mhchem} % used for chemistry and nuclear physics. +\usepackage{multirow} % multirow in a table, for example. +\usepackage{array, makecell} % for additional options in tables and tabular. +\usepackage{hyperref} % link automatically references. +% \usepackage{hycolor} % implements options of colors for hyperref (it ables the user to use colors from xcolor package) +\usepackage[capitalise,nameinlink]{cleveref} % for clever references. That is, for example, for automatically write "Definition 2.13" instead of only "2.13". +\usepackage{graphicx} % for options like \definecolor{}{}{}, \textcolor{}{},... +\usepackage[usenames,x11names]{xcolor} % to customize RGB colors. +\usepackage{colortbl} % for colors in tables. +\usepackage{tcolorbox} % for coloring boxes. +\setlength{\parindent}{0pt} % Indentation disabled. + +\usepackage{float} % to allow using argument [H] in figure environtment + +\setlength\multlinegap{0pt} % disable the margins on \begin{multline} command. +\allowdisplaybreaks % allows to break an align environment in two pages. + +%% colors - subjects %% +\newcommand{\col}{red}% % DEFAULT +\newcommand{\ana}{DeepSkyBlue2}% % analysis +\newcommand{\alg}{Green3}% % algebra +\newcommand{\geo}{Purple2}% % geometry and topology +\newcommand{\apl}{Red2}% % applied mathematics +\newcommand{\pro}{Orange2}% % probability and statistics +\newcommand{\phy}{SlateBlue2}% % physics + +\ExplSyntaxOn +\NewExpandableDocumentCommand{\refcol}{m}{ + \str_case_e:nnF {\FirstWord{#1}}{ + {FM}{\alg} % fundamentals of mathematics + {LA}{\alg} % linear algebra + {RVF}{\ana} % real valued functions + {AS}{\alg} % algebraic structures + {DM}{\alg} % discrete mathematics + {FSV}{\ana} % functions of several variables + {LG}{\geo} % linear geometry + {MA}{\ana} % mathematical analysis + {NM}{\apl} % numerical methods + {CA}{\ana} % complex analysis + {DE}{\apl} % differential equations + {DG}{\geo} % differential geometry + {GT}{\alg} % Galois theory + {P}{\pro} % probability + {S}{\pro} % statistics + {TOP}{\geo} % topology + {AT}{\geo} % algebraic topology + {A}{\alg} % arithmetic + {CAL}{\alg} % commutative algebra + {DS}{\apl} % dynamical systems + {HA}{\ana} % harmonic analysis + {LM}{\pro} % linear models + {NC}{\apl} % numeric calculus + {NIPDE}{\apl} % numeric integration of pde + {PDE}{\apl} % partial differential equations + {RFA}{\ana} % real and functional analysis + {SP}{\pro} % stochastic processes + {ADS}{\apl} % advanced dynamical systems + {AP}{\pro} % advanced probability + {ATFAPDE}{\ana} % advanced topics in functional analysis and pdes + {IEPDE}{\ana} % introduction to evolution pdes + {INLEPDE}{\ana} % introduction to non linear elliptic pdes + {LTLD}{\pro} % limit theorems and large deviations + {SC}{\pro} % stochastic calculus + {INLP}{\phy} % Instabilities and nonlinear phenomena + {MM}{\pro} % Montecarlo methods + {CO}{\apl} % Continuous optimization + {NMPDE}{\apl} % Numerical methods for pdes + {SCO}{\pro} % Stochastic control + {JP}{\pro} % Jump processes + }{\col}% +} +\ExplSyntaxOff +%%%%%%%%%%%%%%%%%%%%%%% + +\newcommand\FirstWord[1]{\@removedots#1:\@nil}% +\newcommand\@removedots{}% +\def\@removedots#1:#2\@nil{#1}% + +\newcommand\changecolor[1]{ + \renewcommand{\col}{\refcol{#1}} + \hypersetup{linkcolor = \col} +} + +%% for references (hyperref) +\hypersetup{ + colorlinks = true, + linkcolor = Blue4, % color of internal links (sections, pages, etc.) + filecolor = cyan, % color for URLs which open local files + citecolor = green, % color for bibliographical citations in text. + urlcolor = cyan, % color of URL links (mail, web) +} +%%%%%%%%%%%%%%%%%%%% + +%% Color box for important theorems +\def\sep{1mm} +\newtcolorbox{important}{colback=\col!5, colframe=\col, left=\sep, right=\sep, top=\sep, bottom=\sep} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +%%%%%%% Enumeration - commands %%%%%%% +\usepackage{enumitem} % for the command [leftmargin=1.15cm] in customized-label enumerations +\renewcommand{\labelenumi}{\arabic{enumi}.} +\renewcommand{\theenumi}{\thetheorem-\arabic{enumi}} + +\renewcommand{\labelenumii}{\roman{enumii})} +\renewcommand{\theenumii}{\theenumi.\roman{enumii})} + +\renewcommand{\labelenumiii}{\alph{enumiii})} +\renewcommand{\theenumiii}{\theenumii.\alph{enumiii})} + + +% for doing things like: +% 1. .............. +% 2. .............. +% 3, 4. ........... +% 5. .............. +\newcommand{\doubleitem}{% + \begingroup + \stepcounter{enumi}% + \edef\tmp{\arabic{enumi}, }% + \stepcounter{enumi} + \edef\tmp{\endgroup\noexpand\item[\tmp\labelenumi]}% + \tmp} + +%% for proving two-way implications +% Usage: +% \begin{itemizeiff} +% First implication ... +% \item Second implication ... +% \end{itemizeiff} +\newlist{itemizeiff}{enumerate}{2} +\setlist[itemizeiff]{ + first=\item[{$\implies\!\!$)}], + label={$\impliedby\!\!$)}, + leftmargin=1.2cm, +} + +\newcommand*\ifftoright{\item[$\implies$:]} +\newcommand*\ifftoleft{\item[$\ \impliedby$:]} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +%%%%% Theorems, definitions,... environments %%%%% +\newtheoremstyle{math_theorems} +{\topsep} % ABOVESPACE +{\topsep} % BELOWSPACE +{} % BODYFONT +{0pt} % INDENT (empty value is the same as 0pt) +{\bfseries} % HEADFONT +{.} % HEADPUNCT +{5pt plus 1pt minus 1pt} % HEADSPACE +{\color{\col}\thmname{#1}\thmnumber{\@ifnotempty{#1}{ }\@upn{#2}}% + \thmnote{{ \bfseries\color{black}(#3)\index{#3}}}} % CUSTOM-HEAD-SPEC + +\theoremstyle{math_theorems} +\newtheorem{theorem}{Theorem} +\newtheorem{lemma}[theorem]{Lemma} +\newtheorem{proposition}[theorem]{Proposition} +\newtheorem{corollary}[theorem]{Corollary} +\newtheorem{axiom}[theorem]{Axiom} +\newtheorem{definition}[theorem]{Definition} +\newtheorem{law}[theorem]{Law} +\newtheorem{principle}[theorem]{Principle} +\newtheorem{model}[theorem]{Model} + +\newtheoremstyle{math_remarks} +{\topsep} % ABOVESPACE +{\topsep} % BELOWSPACE +{} % BODYFONT +{0pt} % INDENT (empty value is the same as 0pt) +{\itshape} % HEADFONT +{.} % HEADPUNCT +{5pt plus 1pt minus 1pt} % HEADSPACE +{\color{\col}\thmname{#1}\thmnote{{ \color{black}(#3)}}} % CUSTOM-HEAD-SPEC + +\theoremstyle{math_remarks} +\newtheorem{remark}{Remark} + +% \renewcommand*{\qed}{{\color{\col}\qed}} +% \renewcommand{\qedsymbol}{\textcolor{\col}{\qed}} +\newcommand*{\QED}[1][$\square$]{% + \color{\col} + \leavevmode\unskip\penalty9999 \hbox{}\nobreak\hfill + \quad\hbox{#1}% +} + +\makeatletter +\renewenvironment{proof}[1][\proofname]{ + \par% + \pushQED{\QED}% + \normalfont% + \topsep5\p@\@plus\p@\@minus\p@\relax% + \trivlist% + \item\relax% + {% + \color{\col}% + \itshape#1\@addpunct{.}}\hspace\labelsep\ignorespaces% +}{% + % \color{\col!30} + \popQED\endtrivlist\@endpefalse% +} +\makeatother + +\newcommand\explanationname{Sketch of the proof} % could be made language-dependent +\newenvironment{sproof}% +{\renewcommand\proofname\explanationname% + \begin{proof}}% + {\end{proof}} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +%%%%%% Extra references %%%%%%% +\makeatletter +\if@cref@capitalise % if we pass the option 'capitalise' on cleveref package + % \crefname{theorem}{\bfseries\color{\col} Theorem}{\bfseries\color{\col} Theorems} + % \crefname{lemma}{\bfseries\color{\col} Lemma}{\bfseries\color{\col} Lemmas} + % \crefname{proposition}{\bfseries\color{\col} Proposition}{\bfseries\color{\col} Propositions} + % \crefname{corollary}{\bfseries\color{\col} Corollary}{\bfseries\color{\col} Corollary} + % \crefname{axiom}{\bfseries\color{\col} Axiom}{\bfseries\color{\col} Axioms} + % \crefname{definition}{\bfseries\color{\col} Definition}{\bfseries\color{\col} Definitions} + % \crefname{law}{\bfseries\color{\col} Law}{\bfseries\color{\col} Laws} + % \crefname{principle}{\bfseries\color{\col} Principle}{\bfseries\color{\col} Principles} + % \crefname{enumi}{\textcolor{\col}{Item}}{\textcolor{\col}{Items}} + % \else + % \crefname{theorem}{\bfseries\color{\col} theorem}{\bfseries\color{\col} theorems} + % \crefname{lemma}{\bfseries\color{\col} lemma}{\bfseries\color{\col} lemmas} + % \crefname{proposition}{\bfseries\color{\col} proposition}{\bfseries\color{\col} propositions} + % \crefname{corollary}{\bfseries\color{\col} corollary}{\bfseries\color{\col} corollary} + % \crefname{axiom}{\bfseries\color{\col} axiom}{\bfseries\color{\col} axioms} + % \crefname{definition}{\bfseries\color{\col} definition}{\bfseries\color{\col} definitions} + % \crefname{law}{\bfseries\color{\col} law}{\bfseries\color{\col} laws} + % \crefname{principle}{\bfseries\color{\col} principle}{\bfseries\color{\col} principles} + % \crefname{enumi}{\textcolor{\col}{item}}{\textcolor{\col}{items}} + \crefname{axiom}{Axiom}{Axioms} +\else + \crefname{axiom}{axiom}{axioms} +\fi +\makeatother + +\newcommand{\mref}[1]{\hypersetup{linkcolor = \refcol{#1}}\ref{#1}\hypersetup{linkcolor = \col}} % custom ref +\newcommand{\mcref}[1]{\hypersetup{linkcolor = \refcol{#1}}\cref{#1}\hypersetup{linkcolor = \col}} % custom cref +% \newcommand{\mnameref}[1]{\hypersetup{linkcolor = \refcol{#1}}\nameref{#1}\hypersetup{linkcolor = \col}} % custom nameref +\newcommand{\mnameref}[1]{\hypersetup{linkcolor = \refcol{#1}}\hyperref[{#1}]{\ref{#1} \nameref{#1}}\hypersetup{linkcolor = \col}} % custom nameref +% \newcommand{\mfullref}[1]{\hypersetup{linkcolor = \refcol{#1}}\hyperref[{#1}]{\ref{#1} \nameref{#1}}\hypersetup{linkcolor = \col}} +% \newcommand{\fullref}[1]{\hypersetup{linkcolor = \refcol{#1}}\hyperref[{#1}]{\autoref{#1} \nameref{#1}}\hypersetup{linkcolor = \col}} +% \crefformat{enumerate}{#2\textcolor{\col}{Item} #1#3} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \ No newline at end of file diff --git a/preamble_formulas.sty b/preamble_math.sty similarity index 50% rename from preamble_formulas.sty rename to preamble_math.sty index 4c6db19..d8a30c5 100644 --- a/preamble_formulas.sty +++ b/preamble_math.sty @@ -1,175 +1,4 @@ \usepackage{amsthm, amsmath, mathtools, amssymb, physics} % for math and physics commands and symbols. -\usepackage[intlimits]{esint} % for more options on integrals. -\usepackage{standalone} % for compiling individually .tex images. -\usepackage[hypcap=false]{caption} % basically for using the command \captionof{}, which is useful in some environments, others than \begin{figure}. -\usepackage{subcaption} % for subfigures, when many captions come into play. -\usepackage{multicol} % organize the whole document in multiple columns. -\usepackage[USenglish]{babel} % for improving use of English and mainly the use of hyphenation. -\usepackage[version=4]{mhchem} % used for chemistry and nuclear physics. -\usepackage{multirow} % multirow in a table, for example. -\usepackage{array, makecell} % for additional options in tables and tabular. -\usepackage{hyperref} % link automatically references. -% \usepackage{hycolor} % implements options of colors for hyperref (it ables the user to use colors from xcolor package) -\usepackage[capitalise,nameinlink]{cleveref} % for clever references. That is, for example, for automatically write "Definition 2.13" instead of only "2.13". -\usepackage{graphicx} % for options like \definecolor{}{}{}, \textcolor{}{},... -\usepackage[usenames,x11names]{xcolor} % to customize RGB colors. -\usepackage{colortbl} % for colors in tables. -\usepackage{tcolorbox} % for coloring boxes. -\setlength{\parindent}{0pt} % Indentation disabled. - -%%%%% tikz images %%%%%% -\usepackage{tikz, pgfplots} % for tikz images. -\usepackage{tkz-euclide} % for getting some useful geometric commands. -\usepackage{tikz-3dplot} % to draw a visual 3d image with tikz (not with pgfplots). -\usepackage[RPvoltages]{circuitikz} % to draw electric circuits with tikz -\usetikzlibrary{arrows,arrows.meta,decorations.pathmorphing,decorations.pathreplacing,decorations.shapes,decorations.markings,patterns,calc,fillbetween,intersections} -\usepgfplotslibrary{fillbetween, polar} -\pgfplotsset{compat=newest} -%%%%%%%%%%%%%%%%%%%%%%%% - -\usepackage{float} % to allow using argument [H] in figure environtment - -\setlength\multlinegap{0pt} % disable the margins on \begin{multline} command. -\allowdisplaybreaks % allows to break an align environment in two pages. - - -%%%%%%%%%%%%%%% Colors %%%%%%%%%%%%%%% -\definecolor{color_blue1}{RGB}{190,190,255} -\definecolor{color_blue2}{RGB}{100,100,255} -\definecolor{color_blue3}{RGB}{0,0,255} -\definecolor{color_blue4}{RGB}{0,0,150} -\definecolor{color_green1}{RGB}{160,240,160} -\definecolor{color_green2}{RGB}{50,200,50} -\definecolor{color_green3}{RGB}{10,150,10} -\definecolor{color_green4}{RGB}{0,80,0} - -%% for creating a rainbow shade -\pgfdeclareverticalshading{rainbow}{100bp}{color(0bp)=(red); - color(25bp)=(red); color(35bp)=(yellow); color(45bp)=(green); - color(55bp)=(cyan); color(65bp)=(blue); color(75bp)=(violet); - color(100bp)=(violet)} -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - -%% colors - subjects %% -\newcommand{\col}{red}% % DEFAULT -\newcommand{\ana}{DeepSkyBlue2}% % analysis -\newcommand{\alg}{Green3}% % algebra -\newcommand{\geo}{Purple2}% % geometry and topology -\newcommand{\apl}{Red2}% % applied mathematics -\newcommand{\pro}{Orange2}% % probability and statistics -\newcommand{\phy}{SlateBlue2}% % physics - -\ExplSyntaxOn -\NewExpandableDocumentCommand{\refcol}{m}{ - \str_case_e:nnF {\FirstWord{#1}}{ - {FM}{\alg} % fundamentals of mathematics - {LA}{\alg} % linear algebra - {RVF}{\ana} % real valued functions - {AS}{\alg} % algebraic structures - {DM}{\alg} % discrete mathematics - {FSV}{\ana} % functions of several variables - {LG}{\geo} % linear geometry - {MA}{\ana} % mathematical analysis - {NM}{\apl} % numerical methods - {CA}{\ana} % complex analysis - {DE}{\apl} % differential equations - {DG}{\geo} % differential geometry - {GT}{\alg} % Galois theory - {P}{\pro} % probability - {S}{\pro} % statistics - {TOP}{\geo} % topology - {AT}{\geo} % algebraic topology - {A}{\alg} % arithmetic - {CAL}{\alg} % commutative algebra - {DS}{\apl} % dynamical systems - {HA}{\ana} % harmonic analysis - {LM}{\pro} % linear models - {NC}{\apl} % numeric calculus - {NIPDE}{\apl} % numeric integration of pde - {PDE}{\apl} % partial differential equations - {RFA}{\ana} % real and functional analysis - {SP}{\pro} % stochastic processes - {ADS}{\apl} % advanced dynamical systems - {AP}{\pro} % advanced probability - {ATFAPDE}{\ana} % advanced topics in functional analysis and pdes - {IEPDE}{\ana} % introduction to evolution pdes - {INLEPDE}{\ana} % introduction to non linear elliptic pdes - {LTLD}{\pro} % limit theorems and large deviations - {SC}{\pro} % stochastic calculus - {INLP}{\phy} % Instabilities and nonlinear phenomena - {MM}{\pro} % Montecarlo methods - {CO}{\apl} % Continuous optimization - {NMPDE}{\apl} % Numerical methods for pdes - {SCO}{\pro} % Stochastic control - {JP}{\pro} % Jump processes - }{\col}% -} -\ExplSyntaxOff -%%%%%%%%%%%%%%%%%%%%%%% - -\newcommand\FirstWord[1]{\@removedots#1:\@nil}% -\newcommand\@removedots{}% -\def\@removedots#1:#2\@nil{#1}% - -\newcommand\changecolor[1]{ - \renewcommand{\col}{\refcol{#1}} - \hypersetup{linkcolor = \col} -} - -%% for references (hyperref) -\hypersetup{ - colorlinks = true, - linkcolor = Blue4, % color of internal links (sections, pages, etc.) - filecolor = cyan, % color for URLs which open local files - citecolor = green, % color for bibliographical citations in text. - urlcolor = cyan, % color of URL links (mail, web) -} -%%%%%%%%%%%%%%%%%%%% - -%% Color box for important theorems -\def\sep{1mm} -\newtcolorbox{important}{colback=\col!5, colframe=\col, left=\sep, right=\sep, top=\sep, bottom=\sep} -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - -%%%%%%% Enumeration - commands %%%%%%% -\usepackage{enumitem} % for the command [leftmargin=1.15cm] in customized-label enumerations -\renewcommand{\labelenumi}{\arabic{enumi}.} -\renewcommand{\theenumi}{\thetheorem-\arabic{enumi}} - -\renewcommand{\labelenumii}{\roman{enumii})} -\renewcommand{\theenumii}{\theenumi.\roman{enumii})} - -\renewcommand{\labelenumiii}{\alph{enumiii})} -\renewcommand{\theenumiii}{\theenumii.\alph{enumiii})} - - -% for doing things like: -% 1. .............. -% 2. .............. -% 3, 4. ........... -% 5. .............. -\newcommand{\doubleitem}{% - \begingroup - \stepcounter{enumi}% - \edef\tmp{\arabic{enumi}, }% - \stepcounter{enumi} - \edef\tmp{\endgroup\noexpand\item[\tmp\labelenumi]}% - \tmp} - - -\newlist{itemizeiff}{enumerate}{2} -\setlist[itemizeiff]{ - first=\item[{$\implies\!\!$)}], - label={$\impliedby\!\!$)}, - leftmargin=1.2cm, -} - -\newcommand*\ifftoright{\item[$\implies$:]} -\newcommand*\ifftoleft{\item[$\ \impliedby$:]} -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - %%%%%%% Math-commands %%%%%%% %%% GENERAL @@ -444,109 +273,4 @@ \cleaders\hbox{$\mkern-2mu\smash-\mkern-2mu$}\hfill \mkern-7mu\raisebox{-3.66pt}[\p@][\p@]{$\mathord\mathchar"017E$}$ } -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - -%%%%% Theorems, definitions,... environments %%%%% -\newtheoremstyle{math_theorems} -{\topsep} % ABOVESPACE -{\topsep} % BELOWSPACE -{} % BODYFONT -{0pt} % INDENT (empty value is the same as 0pt) -{\bfseries} % HEADFONT -{.} % HEADPUNCT -{5pt plus 1pt minus 1pt} % HEADSPACE -{\color{\col}\thmname{#1}\thmnumber{\@ifnotempty{#1}{ }\@upn{#2}}% - \thmnote{{ \bfseries\color{black}(#3)\index{#3}}}} % CUSTOM-HEAD-SPEC - -\theoremstyle{math_theorems} -\newtheorem{theorem}{Theorem} -\newtheorem{lemma}[theorem]{Lemma} -\newtheorem{proposition}[theorem]{Proposition} -\newtheorem{corollary}[theorem]{Corollary} -\newtheorem{axiom}[theorem]{Axiom} -\newtheorem{definition}[theorem]{Definition} -\newtheorem{law}[theorem]{Law} -\newtheorem{principle}[theorem]{Principle} -\newtheorem{model}[theorem]{Model} - -\newtheoremstyle{math_remarks} -{\topsep} % ABOVESPACE -{\topsep} % BELOWSPACE -{} % BODYFONT -{0pt} % INDENT (empty value is the same as 0pt) -{\itshape} % HEADFONT -{.} % HEADPUNCT -{5pt plus 1pt minus 1pt} % HEADSPACE -{\color{\col}\thmname{#1}\thmnote{{ \color{black}(#3)}}} % CUSTOM-HEAD-SPEC - -\theoremstyle{math_remarks} -\newtheorem{remark}{Remark} - -% \renewcommand*{\qed}{{\color{\col}\qed}} -% \renewcommand{\qedsymbol}{\textcolor{\col}{\qed}} -\newcommand*{\QED}[1][$\square$]{% - \color{\col} - \leavevmode\unskip\penalty9999 \hbox{}\nobreak\hfill - \quad\hbox{#1}% -} - -\makeatletter -\renewenvironment{proof}[1][\proofname]{ - \par% - \pushQED{\QED}% - \normalfont% - \topsep5\p@\@plus\p@\@minus\p@\relax% - \trivlist% - \item\relax% - {% - \color{\col}% - \itshape#1\@addpunct{.}}\hspace\labelsep\ignorespaces% -}{% - % \color{\col!30} - \popQED\endtrivlist\@endpefalse% -} -\makeatother - -\newcommand\explanationname{Sketch of the proof} % could be made language-dependent -\newenvironment{sproof}% -{\renewcommand\proofname\explanationname% - \begin{proof}}% - {\end{proof}} -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - -%%%%%% Extra references %%%%%%% -\makeatletter -\if@cref@capitalise % if we pass the option 'capitalise' on cleveref package - % \crefname{theorem}{\bfseries\color{\col} Theorem}{\bfseries\color{\col} Theorems} - % \crefname{lemma}{\bfseries\color{\col} Lemma}{\bfseries\color{\col} Lemmas} - % \crefname{proposition}{\bfseries\color{\col} Proposition}{\bfseries\color{\col} Propositions} - % \crefname{corollary}{\bfseries\color{\col} Corollary}{\bfseries\color{\col} Corollary} - % \crefname{axiom}{\bfseries\color{\col} Axiom}{\bfseries\color{\col} Axioms} - % \crefname{definition}{\bfseries\color{\col} Definition}{\bfseries\color{\col} Definitions} - % \crefname{law}{\bfseries\color{\col} Law}{\bfseries\color{\col} Laws} - % \crefname{principle}{\bfseries\color{\col} Principle}{\bfseries\color{\col} Principles} - % \crefname{enumi}{\textcolor{\col}{Item}}{\textcolor{\col}{Items}} - % \else - % \crefname{theorem}{\bfseries\color{\col} theorem}{\bfseries\color{\col} theorems} - % \crefname{lemma}{\bfseries\color{\col} lemma}{\bfseries\color{\col} lemmas} - % \crefname{proposition}{\bfseries\color{\col} proposition}{\bfseries\color{\col} propositions} - % \crefname{corollary}{\bfseries\color{\col} corollary}{\bfseries\color{\col} corollary} - % \crefname{axiom}{\bfseries\color{\col} axiom}{\bfseries\color{\col} axioms} - % \crefname{definition}{\bfseries\color{\col} definition}{\bfseries\color{\col} definitions} - % \crefname{law}{\bfseries\color{\col} law}{\bfseries\color{\col} laws} - % \crefname{principle}{\bfseries\color{\col} principle}{\bfseries\color{\col} principles} - % \crefname{enumi}{\textcolor{\col}{item}}{\textcolor{\col}{items}} - \crefname{axiom}{Axiom}{Axioms} -\else - \crefname{axiom}{axiom}{axioms} -\fi -\makeatother - -\newcommand{\mref}[1]{\hypersetup{linkcolor = \refcol{#1}}\ref{#1}\hypersetup{linkcolor = \col}} % custom ref -\newcommand{\mcref}[1]{\hypersetup{linkcolor = \refcol{#1}}\cref{#1}\hypersetup{linkcolor = \col}} % custom cref -% \newcommand{\mnameref}[1]{\hypersetup{linkcolor = \refcol{#1}}\nameref{#1}\hypersetup{linkcolor = \col}} % custom nameref -\newcommand{\mnameref}[1]{\hypersetup{linkcolor = \refcol{#1}}\hyperref[{#1}]{\ref{#1} \nameref{#1}}\hypersetup{linkcolor = \col}} % custom nameref -% \newcommand{\mfullref}[1]{\hypersetup{linkcolor = \refcol{#1}}\hyperref[{#1}]{\ref{#1} \nameref{#1}}\hypersetup{linkcolor = \col}} -% \newcommand{\fullref}[1]{\hypersetup{linkcolor = \refcol{#1}}\hyperref[{#1}]{\autoref{#1} \nameref{#1}}\hypersetup{linkcolor = \col}} -% \crefformat{enumerate}{#2\textcolor{\col}{Item} #1#3} -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \ No newline at end of file +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \ No newline at end of file diff --git a/preamble_tikz.sty b/preamble_tikz.sty new file mode 100644 index 0000000..ae7edb0 --- /dev/null +++ b/preamble_tikz.sty @@ -0,0 +1,27 @@ +%%%%% tikz images %%%%%% +\usepackage{tikz, pgfplots} % for tikz images. +\usepackage{tkz-euclide} % for getting some useful geometric commands. +\usepackage{tikz-3dplot} % to draw a visual 3d image with tikz (not with pgfplots). +\usepackage[RPvoltages]{circuitikz} % to draw electric circuits with tikz +\usetikzlibrary{arrows,arrows.meta,decorations.pathmorphing,decorations.pathreplacing,decorations.shapes,decorations.markings,patterns,calc,fillbetween,intersections} +\usepgfplotslibrary{fillbetween, polar} +\pgfplotsset{compat=newest} +%%%%%%%%%%%%%%%%%%%%%%%% + + +%%%%%%%%%%%%%%% Colors %%%%%%%%%%%%%%% +\definecolor{color_blue1}{RGB}{190,190,255} +\definecolor{color_blue2}{RGB}{100,100,255} +\definecolor{color_blue3}{RGB}{0,0,255} +\definecolor{color_blue4}{RGB}{0,0,150} +\definecolor{color_green1}{RGB}{160,240,160} +\definecolor{color_green2}{RGB}{50,200,50} +\definecolor{color_green3}{RGB}{10,150,10} +\definecolor{color_green4}{RGB}{0,80,0} + +%% for creating a rainbow shade +\pgfdeclareverticalshading{rainbow}{100bp}{color(0bp)=(red); + color(25bp)=(red); color(35bp)=(yellow); color(45bp)=(green); + color(55bp)=(cyan); color(65bp)=(blue); color(75bp)=(violet); + color(100bp)=(violet)} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%